Loewner chains and parametric representation in several complex variables

Let B be the unit ball of C n with respect to an arbitrary norm. We study certain properties of Loewner chains and their transition mappings on the unit ball  B. We show that any Loewner chain f( z, t) and the transition mapping v( z, s, t) associated to f( z, t) satisfy locally Lipschitz conditions...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Journal of mathematical analysis and applications Ročník 281; číslo 2; s. 425 - 438
Hlavní autori: Graham, Ian, Kohr, Gabriela, Kohr, Mirela
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: San Diego, CA Elsevier Inc 15.05.2003
Elsevier
Predmet:
Exact sciences and technology
Loewner chain
Loewner differential equation
Mathematical analysis
Mathematics
Parametric representation
Sciences and techniques of general use
Several complex variables and analytic spaces
Transition mapping
Univalent mapping
Loewner chain
Univalent mapping
Parametric representation
Loewner differential equation
Transition mapping
Parametric method
Lipschitz condition
Mathematical analysis
Loewne chain
Complex variable function
ISSN:0022-247X, 1096-0813
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Abstract Let B be the unit ball of C n with respect to an arbitrary norm. We study certain properties of Loewner chains and their transition mappings on the unit ball  B. We show that any Loewner chain f( z, t) and the transition mapping v( z, s, t) associated to f( z, t) satisfy locally Lipschitz conditions in t locally uniformly with respect to z∈ B. Moreover, we prove that a mapping f∈ H( B) has parametric representation if and only if there exists a Loewner chain f( z, t) such that the family { e − t f( z, t)} t⩾0 is a normal family on B and f( z)= f( z,0) for z∈ B. Also we show that univalent solutions f( z, t) of the generalized Loewner differential equation in higher dimensions are unique when { e − t f( z, t)} t⩾0 is a normal family on  B. Finally we show that the set S 0( B) of mappings which have parametric representation on B is compact.
AbstractList Let B be the unit ball of C n with respect to an arbitrary norm. We study certain properties of Loewner chains and their transition mappings on the unit ball  B. We show that any Loewner chain f( z, t) and the transition mapping v( z, s, t) associated to f( z, t) satisfy locally Lipschitz conditions in t locally uniformly with respect to z∈ B. Moreover, we prove that a mapping f∈ H( B) has parametric representation if and only if there exists a Loewner chain f( z, t) such that the family { e − t f( z, t)} t⩾0 is a normal family on B and f( z)= f( z,0) for z∈ B. Also we show that univalent solutions f( z, t) of the generalized Loewner differential equation in higher dimensions are unique when { e − t f( z, t)} t⩾0 is a normal family on  B. Finally we show that the set S 0( B) of mappings which have parametric representation on B is compact.
Author Kohr, Gabriela
Graham, Ian
Kohr, Mirela
Author_xml – sequence: 1
  givenname: Ian
  surname: Graham
  fullname: Graham, Ian
  email: graham@math.toronto.edu
  organization: Department of Mathematics, University of Toronto, Toronto, ON M5S 3G3, Canada
– sequence: 2
  givenname: Gabriela
  surname: Kohr
  fullname: Kohr, Gabriela
  email: gkohr@math.ubbcluj.ro
  organization: Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 M. Kogălniceanu Str., 3400 Cluj-Napoca, Romania
– sequence: 3
  givenname: Mirela
  surname: Kohr
  fullname: Kohr, Mirela
  email: mkohr@math.ubbcluj.ro
  organization: Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 M. Kogălniceanu Str., 3400 Cluj-Napoca, Romania
BackLink http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=14891142$$DView record in Pascal Francis
BookMark eNqFkE9Lw0AQRxepYFv9CEIugh6is7vZNMGDSPFPoeBBBW_LdHeCK-km7Iaq3960EQUvnuby3g_mTdjIN54YO-ZwzoHnF48AQqQim72cgjwD4GKW5ntszKHMUyi4HLHxD3LAJjG-9RBXMz5mi2VD755CYl7R-Zigt0mLAdfUBWeSQG2gSL7DzjU-cT6JtKGAdWKadVvTR7LB4HBVUzxk-xXWkY6-75Q93948ze_T5cPdYn69TE0GsksVGcltAVTKKrMyA4Iqt7akFYqykJkqKwFcqpXkCitlQCqyhpQEUWBRVnLKTobdFqPBugrojYu6DW6N4VPzrCg5z0TPqYEzoYkxUPWLgN5207tuehtFg9S7bjrvvcs_nnHD-11AV_9rXw029Qk2joKOxpE3ZF0g02nbuH8WvgAOA4oD
CODEN JMANAK
CitedBy_id crossref_primary_10_1080_17476933_2022_2107634
crossref_primary_10_1016_j_jmaa_2011_02_080
crossref_primary_10_1007_s11854_008_0037_1
crossref_primary_10_1016_j_jmaa_2011_07_064
crossref_primary_10_1016_S0252_9602_18_30782_3
crossref_primary_10_1007_s11401_019_0184_y
crossref_primary_10_1007_s11785_012_0273_3
crossref_primary_10_1007_s40315_014_0102_y
crossref_primary_10_1007_s40315_022_00467_z
crossref_primary_10_1016_S0252_9602_17_30033_4
crossref_primary_10_1080_17476933_2020_1743985
crossref_primary_10_1016_j_jmaa_2023_127767
crossref_primary_10_1080_17476933_2013_856422
crossref_primary_10_1007_s00208_013_0998_y
crossref_primary_10_1016_j_jmaa_2006_10_036
crossref_primary_10_1016_j_camwa_2011_02_011
crossref_primary_10_1007_s10114_016_5762_2
crossref_primary_10_1016_j_jmaa_2012_01_035
crossref_primary_10_1007_s11785_010_0106_1
crossref_primary_10_1016_j_jmaa_2011_12_023
crossref_primary_10_1007_s11785_010_0093_2
crossref_primary_10_1007_s11785_015_0525_0
crossref_primary_10_1007_s11425_012_4376_0
crossref_primary_10_1016_j_jmaa_2005_08_002
crossref_primary_10_1080_17476933_2017_1361939
crossref_primary_10_1155_2014_807026
crossref_primary_10_1007_s00208_009_0340_x
crossref_primary_10_1002_mana_200510433
crossref_primary_10_1007_s11425_017_9221_8
crossref_primary_10_1080_02781070500086636
crossref_primary_10_1080_17476933_2012_746966
crossref_primary_10_1007_s10473_020_0603_x
crossref_primary_10_1007_s00025_019_1080_1
crossref_primary_10_1007_s11464_022_0309_6
crossref_primary_10_1016_j_jmaa_2014_07_084
crossref_primary_10_1080_17476933_2024_2355153
crossref_primary_10_1016_j_jmaa_2010_08_057
crossref_primary_10_1007_s40315_020_00353_6
crossref_primary_10_1016_j_jmaa_2007_04_044
crossref_primary_10_1007_s00025_019_0988_9
crossref_primary_10_1007_s11785_015_0461_z
crossref_primary_10_1007_s11785_015_0468_5
crossref_primary_10_1007_s00025_017_0650_3
crossref_primary_10_1016_j_jmaa_2009_01_056
crossref_primary_10_1007_s00365_015_9302_6
crossref_primary_10_1007_s00025_018_0837_2
crossref_primary_10_1007_s00208_009_0429_2
crossref_primary_10_1080_17476933_2019_1662406
crossref_primary_10_1007_s11464_015_0496_5
crossref_primary_10_1007_s00025_021_01500_8
crossref_primary_10_1007_s40315_019_00289_6
Cites_doi 10.1080/02781070290002921
10.2140/pjm.2000.194.359
10.1307/mmj/1022636749
10.1090/S0002-9947-99-02219-9
10.4064/ap81-1-8
10.1007/BF01344545
10.2140/pjm.1995.168.33
10.2140/pjm.1973.46.575
10.1006/jmaa.2000.6843
10.4153/CJM-2002-011-2
10.1080/17476930108815360
10.2140/pjm.1975.57.271
ContentType Journal Article
Copyright 2003 Elsevier Science (USA)
2003 INIST-CNRS
Copyright_xml – notice: 2003 Elsevier Science (USA)
– notice: 2003 INIST-CNRS
DBID 6I.
AAFTH
AAYXX
CITATION
IQODW
DOI 10.1016/S0022-247X(03)00127-6
DatabaseName ScienceDirect Open Access Titles
Elsevier:ScienceDirect:Open Access
CrossRef
Pascal-Francis
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 1096-0813
EndPage 438
ExternalDocumentID 14891142
10_1016_S0022_247X_03_00127_6
S0022247X03001276
GroupedDBID --K
--M
--Z
-~X
.~1
0R~
0SF
1B1
1RT
1~.
1~5
29L
4.4
457
4G.
5GY
5VS
6I.
6TJ
7-5
71M
85S
8P~
9JN
AABNK
AACTN
AAEDT
AAEDW
AAFTH
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AASFE
AAXUO
ABAOU
ABEFU
ABFNM
ABJNI
ABMAC
ABVKL
ABXDB
ABYKQ
ACAZW
ACDAQ
ACGFS
ACRLP
ADBBV
ADEZE
ADFGL
ADIYS
ADMUD
AEBSH
AEKER
AENEX
AETEA
AEXQZ
AFFNX
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AI.
AIEXJ
AIGVJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
ARUGR
ASPBG
AVWKF
AXJTR
AZFZN
BKOJK
BLXMC
CAG
COF
CS3
DM4
EBS
EFBJH
EFLBG
EJD
EO8
EO9
EP2
EP3
F5P
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
G8K
GBLVA
HVGLF
HZ~
H~9
IHE
IXB
J1W
KOM
LG5
M25
M41
MCRUF
MHUIS
MO0
MVM
N9A
NCXOZ
O-L
O9-
OAUVE
OHT
OK1
OZT
P-8
P-9
P2P
PC.
Q38
R2-
RIG
RNS
ROL
RPZ
SDF
SDG
SDP
SES
SEW
SPC
SPCBC
SSW
SSZ
T5K
TN5
TWZ
UPT
VH1
VOH
WH7
WUQ
XOL
XPP
YQT
YYP
ZCG
ZMT
ZU3
~G-
9DU
AATTM
AAXKI
AAYWO
AAYXX
ABDPE
ABUFD
ABWVN
ACLOT
ACRPL
ACVFH
ADCNI
ADNMO
ADVLN
ADXHL
AEIPS
AEUPX
AFJKZ
AFPUW
AGQPQ
AIGII
AIIUN
AKBMS
AKRWK
AKYEP
ANKPU
APXCP
CITATION
EFKBS
~HD
AFXIZ
AGCQF
AGRNS
BNPGV
IQODW
SSH
ID FETCH-LOGICAL-c403t-5ec31d80e93f4d340e0f6dd9eba2983459f20135b315af5c035edce53028a89f3
ISICitedReferencesCount 70
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000183591300002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0022-247X
IngestDate Mon Jul 21 09:17:19 EDT 2025
Sat Nov 29 03:47:28 EST 2025
Tue Nov 18 22:36:57 EST 2025
Fri Feb 23 02:23:19 EST 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 2
Keywords Loewner chain
Univalent mapping
Parametric representation
Loewner differential equation
Transition mapping
Parametric method
Lipschitz condition
Mathematical analysis
Loewne chain
Complex variable function
Language English
License http://www.elsevier.com/open-access/userlicense/1.0
https://www.elsevier.com/tdm/userlicense/1.0
https://www.elsevier.com/open-access/userlicense/1.0
CC BY 4.0
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c403t-5ec31d80e93f4d340e0f6dd9eba2983459f20135b315af5c035edce53028a89f3
OpenAccessLink https://dx.doi.org/10.1016/S0022-247X(03)00127-6
PageCount 14
ParticipantIDs pascalfrancis_primary_14891142
crossref_primary_10_1016_S0022_247X_03_00127_6
crossref_citationtrail_10_1016_S0022_247X_03_00127_6
elsevier_sciencedirect_doi_10_1016_S0022_247X_03_00127_6
PublicationCentury 2000
PublicationDate 2003-05-15
PublicationDateYYYYMMDD 2003-05-15
PublicationDate_xml – month: 05
  year: 2003
  text: 2003-05-15
  day: 15
PublicationDecade 2000
PublicationPlace San Diego, CA
PublicationPlace_xml – name: San Diego, CA
PublicationTitle Journal of mathematical analysis and applications
PublicationYear 2003
Publisher Elsevier Inc
Elsevier
Publisher_xml – name: Elsevier Inc
– name: Elsevier
References Hamada, Kohr (BIB013) 2001; 55
Poreda (BIB025) 1987; 41
Graham, Hamada, Kohr, Suffridge (BIB006) 2002; 50
Hamada, Kohr (BIB014) 2001; 44
Suffridge (BIB030) 1973; 46
Becker (BIB001) 1976; 285
H. Hamada, G. Kohr, Loewner chains and quasiconformal extension of holomorphic mappings, Ann. Polon. Math., to appear
Kubicka, Poreda (BIB018) 1988; 21
Ren, Ma (BIB027) 1995; 34
Poreda (BIB026) 1989; 128
Roper, Suffridge (BIB029) 1999; 351
Graham, Hamada, Kohr (BIB005) 2002; 54
Pfaltzgraff (BIB021) 1975; 1
Kohr, Liczberski (BIB017) 1998
Graham, Kohr, Kohr (BIB009) 2000; 247
Pommerenke (BIB024) 1975
Royden (BIB028) 1988
I. Graham, G. Kohr, Geometric Function Theory in One and Higher Dimensions, Dekker, New York, to appear
Hamada, Kohr (BIB012) 2000; 42
Kohr (BIB016) 2001; 46
Narasimhan (BIB019) 1971
Pfaltzgraff (BIB020) 1974; 210
Becker (BIB002) 1980
Chuaqui (BIB004) 1995; 168
H. Hamada, Univalence and quasiconformal extension of holomorphic maps on balanced pseudoconvex domains, preprint
Hamada (BIB010) 2000; 194
Pfaltzgraff (BIB022) 1990; 11
Brodskii (BIB003) 1983
Graham, Kohr (BIB007) 2002; 47
Pfaltzgraff, Suffridge (BIB023) 1975; 57
Royden (10.1016/S0022-247X(03)00127-6_BIB028) 1988
Hamada (10.1016/S0022-247X(03)00127-6_BIB013) 2001; 55
Kohr (10.1016/S0022-247X(03)00127-6_BIB017) 1998
Graham (10.1016/S0022-247X(03)00127-6_BIB009) 2000; 247
Narasimhan (10.1016/S0022-247X(03)00127-6_BIB019) 1971
Pfaltzgraff (10.1016/S0022-247X(03)00127-6_BIB022) 1990; 11
Poreda (10.1016/S0022-247X(03)00127-6_BIB026) 1989; 128
Kohr (10.1016/S0022-247X(03)00127-6_BIB016) 2001; 46
Graham (10.1016/S0022-247X(03)00127-6_BIB005) 2002; 54
10.1016/S0022-247X(03)00127-6_BIB008
Brodskii (10.1016/S0022-247X(03)00127-6_BIB003) 1983
Hamada (10.1016/S0022-247X(03)00127-6_BIB012) 2000; 42
Roper (10.1016/S0022-247X(03)00127-6_BIB029) 1999; 351
Graham (10.1016/S0022-247X(03)00127-6_BIB006) 2002; 50
Poreda (10.1016/S0022-247X(03)00127-6_BIB025) 1987; 41
Becker (10.1016/S0022-247X(03)00127-6_BIB001) 1976; 285
10.1016/S0022-247X(03)00127-6_BIB011
Hamada (10.1016/S0022-247X(03)00127-6_BIB010) 2000; 194
Pfaltzgraff (10.1016/S0022-247X(03)00127-6_BIB020) 1974; 210
Pfaltzgraff (10.1016/S0022-247X(03)00127-6_BIB023) 1975; 57
Pfaltzgraff (10.1016/S0022-247X(03)00127-6_BIB021) 1975; 1
Graham (10.1016/S0022-247X(03)00127-6_BIB007) 2002; 47
Ren (10.1016/S0022-247X(03)00127-6_BIB027) 1995; 34
Chuaqui (10.1016/S0022-247X(03)00127-6_BIB004) 1995; 168
Kubicka (10.1016/S0022-247X(03)00127-6_BIB018) 1988; 21
Suffridge (10.1016/S0022-247X(03)00127-6_BIB030) 1973; 46
Becker (10.1016/S0022-247X(03)00127-6_BIB002) 1980
Hamada (10.1016/S0022-247X(03)00127-6_BIB014) 2001; 44
Pommerenke (10.1016/S0022-247X(03)00127-6_BIB024) 1975
10.1016/S0022-247X(03)00127-6_BIB015
References_xml – volume: 285
  start-page: 66
  year: 1976
  end-page: 74
  ident: BIB001
  article-title: Über die Lösungsstruktur einer differentialgleichung in der konformen Abbildung
  publication-title: J. Reine Angew. Math.
– year: 1998
  ident: BIB017
  publication-title: Univalent Mappings of Several Complex Variables
– year: 1988
  ident: BIB028
  publication-title: Real Analysis
– volume: 50
  start-page: 37
  year: 2002
  end-page: 55
  ident: BIB006
  article-title: Extension operators for locally univalent mappings
  publication-title: Michigan Math. J.
– volume: 44
  start-page: 281
  year: 2001
  end-page: 297
  ident: BIB014
  article-title: The growth theorem and quasiconformal extension of strongly spirallike mappings of type
  publication-title: Complex Variables
– volume: 47
  start-page: 59
  year: 2002
  end-page: 72
  ident: BIB007
  article-title: An extension theorem and subclasses of univalent mappings in several complex variables
  publication-title: Complex Variables
– volume: 168
  start-page: 33
  year: 1995
  end-page: 48
  ident: BIB004
  article-title: Applications of subordination chains to starlike mappings in
  publication-title: Pacific J. Math.
– volume: 11
  start-page: 46
  year: 1990
  ident: BIB022
  article-title: Loewner theory in
  publication-title: Amer. Math. Soc.
– year: 1975
  ident: BIB024
  publication-title: Univalent Functions
– volume: 1
  start-page: 13
  year: 1975
  end-page: 25
  ident: BIB021
  article-title: Subordination chains and quasiconformal extension of holomorphic maps in
  publication-title: Ann. Acad. Sci. Fenn. Ser. A
– start-page: 37
  year: 1980
  end-page: 77
  ident: BIB002
  article-title: Conformal mappings with quasiconformal extensions
  publication-title: Aspects of Contemporary Complex Analysis
– reference: I. Graham, G. Kohr, Geometric Function Theory in One and Higher Dimensions, Dekker, New York, to appear
– volume: 54
  start-page: 324
  year: 2002
  end-page: 351
  ident: BIB005
  article-title: Parametric representation of univalent mappings in several complex variables
  publication-title: Canad. J. Math.
– volume: 128
  start-page: 295
  year: 1989
  end-page: 304
  ident: BIB026
  article-title: On the univalent subordination chains of holomorphic mappings in Banach spaces
  publication-title: Comment. Math.
– year: 1971
  ident: BIB019
  publication-title: Several Complex Variables
– volume: 247
  start-page: 448
  year: 2000
  end-page: 465
  ident: BIB009
  article-title: Loewner chains and the Roper–Suffridge extension operator
  publication-title: J. Math. Anal. Appl.
– volume: 34
  start-page: 545
  year: 1995
  end-page: 556
  ident: BIB027
  article-title: Quasiconformal extension of biholomorphic mappings of several complex variables
  publication-title: J. Fudan Univ. Nat. Sci.
– volume: 55
  start-page: 61
  year: 2001
  end-page: 80
  ident: BIB013
  article-title: Subordination chains and univalence of holomorphic mappings on bounded balanced pseudoconvex domains
  publication-title: Ann. Univ. Mariae Curie-Skłodowska Sect. A
– volume: 42
  start-page: 153
  year: 2000
  end-page: 161
  ident: BIB012
  article-title: Subordination chains and the growth theorem of spirallike mappings
  publication-title: Mathematica (Cluj)
– reference: H. Hamada, Univalence and quasiconformal extension of holomorphic maps on balanced pseudoconvex domains, preprint
– volume: 41
  start-page: 105
  year: 1987
  end-page: 113
  ident: BIB025
  article-title: On the univalent holomorphic maps of the unit polydisc of
  publication-title: Ann. Univ. Mariae Curie-Skłodowska Sect. A
– volume: 46
  start-page: 743
  year: 2001
  end-page: 760
  ident: BIB016
  article-title: Using the method of Löwner chains to introduce some subclasses of biholomorphic mappings in
  publication-title: Rev. Roumaine Math. Pures Appl.
– volume: 21
  start-page: 345
  year: 1988
  end-page: 355
  ident: BIB018
  article-title: On the parametric representation of starlike maps of the unit ball in
  publication-title: Demonstratio Math.
– volume: 57
  start-page: 271
  year: 1975
  end-page: 279
  ident: BIB023
  article-title: Close-to-starlike holomorphic functions of several variables
  publication-title: Pacific J. Math.
– volume: 46
  start-page: 474
  year: 1973
  end-page: 489
  ident: BIB030
  article-title: Starlike and convex maps in Banach spaces
  publication-title: Pacific J. Math.
– volume: 210
  start-page: 55
  year: 1974
  end-page: 68
  ident: BIB020
  article-title: Subordination chains and univalence of holomorphic mappings in
  publication-title: Math. Ann.
– volume: 351
  start-page: 1803
  year: 1999
  end-page: 1833
  ident: BIB029
  article-title: Convexity properties of holomorphic mappings in
  publication-title: Trans. Amer. Math. Soc.
– start-page: 30
  year: 1983
  end-page: 34
  ident: BIB003
  article-title: Quasiconformal extension of biholomorphic mappings
  publication-title: Theory of Mappings and Approximation of Functions
– volume: 194
  start-page: 359
  year: 2000
  end-page: 371
  ident: BIB010
  article-title: Starlike mappings on bounded balanced domains with
  publication-title: Pacific J. Math.
– reference: H. Hamada, G. Kohr, Loewner chains and quasiconformal extension of holomorphic mappings, Ann. Polon. Math., to appear
– volume: 46
  start-page: 743
  year: 2001
  ident: 10.1016/S0022-247X(03)00127-6_BIB016
  article-title: Using the method of Löwner chains to introduce some subclasses of biholomorphic mappings in Cn
  publication-title: Rev. Roumaine Math. Pures Appl.
– start-page: 30
  year: 1983
  ident: 10.1016/S0022-247X(03)00127-6_BIB003
  article-title: Quasiconformal extension of biholomorphic mappings
– volume: 11
  start-page: 46
  year: 1990
  ident: 10.1016/S0022-247X(03)00127-6_BIB022
  article-title: Loewner theory in Cn
  publication-title: Amer. Math. Soc.
– year: 1975
  ident: 10.1016/S0022-247X(03)00127-6_BIB024
– volume: 47
  start-page: 59
  year: 2002
  ident: 10.1016/S0022-247X(03)00127-6_BIB007
  article-title: An extension theorem and subclasses of univalent mappings in several complex variables
  publication-title: Complex Variables
  doi: 10.1080/02781070290002921
– year: 1998
  ident: 10.1016/S0022-247X(03)00127-6_BIB017
– year: 1971
  ident: 10.1016/S0022-247X(03)00127-6_BIB019
– volume: 194
  start-page: 359
  year: 2000
  ident: 10.1016/S0022-247X(03)00127-6_BIB010
  article-title: Starlike mappings on bounded balanced domains with C1-plurisubharmonic defining functions
  publication-title: Pacific J. Math.
  doi: 10.2140/pjm.2000.194.359
– volume: 285
  start-page: 66
  year: 1976
  ident: 10.1016/S0022-247X(03)00127-6_BIB001
  article-title: Über die Lösungsstruktur einer differentialgleichung in der konformen Abbildung
  publication-title: J. Reine Angew. Math.
– ident: 10.1016/S0022-247X(03)00127-6_BIB008
– volume: 50
  start-page: 37
  year: 2002
  ident: 10.1016/S0022-247X(03)00127-6_BIB006
  article-title: Extension operators for locally univalent mappings
  publication-title: Michigan Math. J.
  doi: 10.1307/mmj/1022636749
– ident: 10.1016/S0022-247X(03)00127-6_BIB011
– volume: 351
  start-page: 1803
  year: 1999
  ident: 10.1016/S0022-247X(03)00127-6_BIB029
  article-title: Convexity properties of holomorphic mappings in Cn
  publication-title: Trans. Amer. Math. Soc.
  doi: 10.1090/S0002-9947-99-02219-9
– ident: 10.1016/S0022-247X(03)00127-6_BIB015
  doi: 10.4064/ap81-1-8
– volume: 21
  start-page: 345
  year: 1988
  ident: 10.1016/S0022-247X(03)00127-6_BIB018
  article-title: On the parametric representation of starlike maps of the unit ball in Cn into Cn
  publication-title: Demonstratio Math.
– volume: 34
  start-page: 545
  year: 1995
  ident: 10.1016/S0022-247X(03)00127-6_BIB027
  article-title: Quasiconformal extension of biholomorphic mappings of several complex variables
  publication-title: J. Fudan Univ. Nat. Sci.
– year: 1988
  ident: 10.1016/S0022-247X(03)00127-6_BIB028
– volume: 41
  start-page: 105
  year: 1987
  ident: 10.1016/S0022-247X(03)00127-6_BIB025
  article-title: On the univalent holomorphic maps of the unit polydisc of Cn which have the parametric representation, I—the geometrical properties
  publication-title: Ann. Univ. Mariae Curie-Skłodowska Sect. A
– volume: 210
  start-page: 55
  year: 1974
  ident: 10.1016/S0022-247X(03)00127-6_BIB020
  article-title: Subordination chains and univalence of holomorphic mappings in Cn
  publication-title: Math. Ann.
  doi: 10.1007/BF01344545
– volume: 168
  start-page: 33
  year: 1995
  ident: 10.1016/S0022-247X(03)00127-6_BIB004
  article-title: Applications of subordination chains to starlike mappings in Cn
  publication-title: Pacific J. Math.
  doi: 10.2140/pjm.1995.168.33
– volume: 46
  start-page: 474
  year: 1973
  ident: 10.1016/S0022-247X(03)00127-6_BIB030
  article-title: Starlike and convex maps in Banach spaces
  publication-title: Pacific J. Math.
  doi: 10.2140/pjm.1973.46.575
– volume: 247
  start-page: 448
  year: 2000
  ident: 10.1016/S0022-247X(03)00127-6_BIB009
  article-title: Loewner chains and the Roper–Suffridge extension operator
  publication-title: J. Math. Anal. Appl.
  doi: 10.1006/jmaa.2000.6843
– start-page: 37
  year: 1980
  ident: 10.1016/S0022-247X(03)00127-6_BIB002
  article-title: Conformal mappings with quasiconformal extensions
– volume: 54
  start-page: 324
  year: 2002
  ident: 10.1016/S0022-247X(03)00127-6_BIB005
  article-title: Parametric representation of univalent mappings in several complex variables
  publication-title: Canad. J. Math.
  doi: 10.4153/CJM-2002-011-2
– volume: 55
  start-page: 61
  year: 2001
  ident: 10.1016/S0022-247X(03)00127-6_BIB013
  article-title: Subordination chains and univalence of holomorphic mappings on bounded balanced pseudoconvex domains
  publication-title: Ann. Univ. Mariae Curie-Skłodowska Sect. A
– volume: 1
  start-page: 13
  year: 1975
  ident: 10.1016/S0022-247X(03)00127-6_BIB021
  article-title: Subordination chains and quasiconformal extension of holomorphic maps in Cn
  publication-title: Ann. Acad. Sci. Fenn. Ser. A
– volume: 42
  start-page: 153
  year: 2000
  ident: 10.1016/S0022-247X(03)00127-6_BIB012
  article-title: Subordination chains and the growth theorem of spirallike mappings
  publication-title: Mathematica (Cluj)
– volume: 44
  start-page: 281
  year: 2001
  ident: 10.1016/S0022-247X(03)00127-6_BIB014
  article-title: The growth theorem and quasiconformal extension of strongly spirallike mappings of type α
  publication-title: Complex Variables
  doi: 10.1080/17476930108815360
– volume: 57
  start-page: 271
  year: 1975
  ident: 10.1016/S0022-247X(03)00127-6_BIB023
  article-title: Close-to-starlike holomorphic functions of several variables
  publication-title: Pacific J. Math.
  doi: 10.2140/pjm.1975.57.271
– volume: 128
  start-page: 295
  year: 1989
  ident: 10.1016/S0022-247X(03)00127-6_BIB026
  article-title: On the univalent subordination chains of holomorphic mappings in Banach spaces
  publication-title: Comment. Math.
SSID ssj0011571
Score 1.9980503
Snippet Let B be the unit ball of C n with respect to an arbitrary norm. We study certain properties of Loewner chains and their transition mappings on the unit ball ...
SourceID pascalfrancis
crossref
elsevier
SourceType Index Database
Enrichment Source
Publisher
StartPage 425
SubjectTerms Exact sciences and technology
Loewner chain
Loewner differential equation
Mathematical analysis
Mathematics
Parametric representation
Sciences and techniques of general use
Several complex variables and analytic spaces
Transition mapping
Univalent mapping
Title Loewner chains and parametric representation in several complex variables
URI https://dx.doi.org/10.1016/S0022-247X(03)00127-6
Volume 281
WOSCitedRecordID wos000183591300002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVESC
  databaseName: Elsevier SD Freedom Collection Journals 2021
  customDbUrl:
  eissn: 1096-0813
  dateEnd: 20180131
  omitProxy: false
  ssIdentifier: ssj0011571
  issn: 0022-247X
  databaseCode: AIEXJ
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1LbxMxELZCygGEEE_RApUPVAJVS71rO2sfI1RIgRQERcpttfZ6pUhhGyVpyJlfzvixjxaqwIHLKrLiteTv2_HYnvkGoRcqKZOcKR1xsH4RUwy-uZyLSBUk1joV5UCWrthEenoqJhP5udf7WefCrGdpVYnNRs7_K9TQBmDb1Nl_gLt5KTTAbwAdngA7PP8K-I_n5kdlFjal14a_OCGA3IZgWS3-QydiWSccuShHWBrtuZQPLjebwzXsnm0-1fIav_V7I_TqZAaCponTfO1chjdxPV-Go-HYWaKWhx8-jVz8xbtcwU59ll9tH08XdWt9IOHC_3xKpj8lC0t61-rChjdh6aRrdRNfqSXQK-nYUOYzocNyzLz4y2-W3h86fG3efWDLbB0k0t2lR39Q176y6jWxiLAflDah-AbaSVIuRR_tDE-OJ--bu6iYp3GtOW9HavPAjtrhXxL6Kgx9nYdzZ54vAZnSF0zpeDFn99DdACMeetrcRz1TPUC3xw2ky4foJBAIewJhQBa3BMKXCYSnFQ4EwoFAuCHQI_Tt7fHZm1EUCm5EmhG6irjRNC4EMZKWrKCMGFIOikIalSdSUMZlCf4i5YrGPC-5JpTbIGJbeErkQpb0MepX55V5grAQiig7tRJ27ElOwLprBd65svt3LeJdxOpJynRQo7dFUWZZG3YIc5vZuc0IzdzcZoNd9LrpNvdyLNs6iBqBLPiU3lfMgEjbuu5fQqwdMDBmb9sfnqJb7QfyDPVXiwvzHN3U69V0udgPPPsFseeb7A
linkProvider Elsevier
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Loewner+chains+and+parametric+representation+in+several+complex+variables&rft.jtitle=Journal+of+mathematical+analysis+and+applications&rft.au=GRAHAM%2C+Ian&rft.au=KOHR%2C+Gabriela&rft.au=KOHR%2C+Mirela&rft.date=2003-05-15&rft.pub=Elsevier&rft.issn=0022-247X&rft.volume=281&rft.issue=2&rft.spage=425&rft.epage=438&rft_id=info:doi/10.1016%2FS0022-247X%2803%2900127-6&rft.externalDBID=n%2Fa&rft.externalDocID=14891142
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0022-247X&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0022-247X&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0022-247X&client=summon