Search Results - Global boundary behavior of holomorphic functions of several complex variables*

Bounded holomorphic functions and maps with some boundary behavior

Authors: Toshio Matsushima

Source: Journal of Mathematical Analysis and Applications. 285:691-707

Subject Terms: linear cluster set of positive measure, Global boundary behavior of holomorphic functions of several complex variables, Applied Mathematics, bounded holomorphic function, 0103 physical sciences, Boundary behavior of holomorphic functions of several complex variables, bounded holomorphic map with wild boundary behavior, 0101 mathematics, 01 natural sciences, theorems of Fatou type, Analysis, boundary behavior of holomorphic mapping

File Description: application/xml

Access URL: https://zbmath.org/1992576
https://doi.org/10.1016/s0022-247x(03)00471-2
https://www.sciencedirect.com/science/article/pii/S0022247X03004712

The restrictions of functions holomorphic in a domain to curves lying on its boundary, and discrete $ \operatorname{SL}_2(\mathbb R)$-spectra: The restrictions of functions holomorphic in a domain to curves lying on its boundary, and discrete \(SL_2(\mathbb{R})\)-spectra

Authors: Yu A Neretin

Source: Izvestiya: Mathematics. 62:493-513

Subject Terms: polynomial growth, Holomorphic functions of several complex variables, Global boundary behavior of holomorphic functions of several complex variables, holomorphic function, Boundary behavior of holomorphic functions of several complex variables, restriction, 0101 mathematics, 01 natural sciences, Operations with distributions and generalized functions

File Description: application/xml

Access URL: https://zbmath.org/1252647
https://doi.org/10.1070/im1998v062n03abeh000202
http://ui.adsabs.harvard.edu/abs/1998IzMat..62..493N/abstract

Holomorphic functions which are highly nonintegrable at the boundary

Authors: Josip Globevnik

Source: Israel Journal of Mathematics. 115:195-203

Subject Terms: convex domain, Global boundary behavior of holomorphic functions of several complex variables, 0101 mathematics, holomorhpic function, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/1436104
https://doi.org/10.1007/bf02810586
https://link.springer.com/article/10.1007/BF02810586
https://link.springer.com/content/pdf/10.1007/BF02810586.pdf

Tangential boundary limits and exceptional sets for holomorphic functions in Dirichlet-type spaces

Authors: Sueiro, Juan

Source: Mathematische Annalen. 286:661-678

Subject Terms: Dirichlet forms, 510.mathematics, fractional Cauchy integrals, Global boundary behavior of holomorphic functions of several complex variables, Picard-type theorems and generalizations for several complex variables, existence of tangential boundary limits, Boundary behavior of holomorphic functions of several complex variables, exceptional sets, 0101 mathematics, 16. Peace & justice, 01 natural sciences, Article, approach regions

File Description: application/xml; image/jpeg; application/pdf

Access URL: https://link.springer.com/article/10.1007/BF01453595

Reflection principle and boundary properties of holomorphic mappings

Authors: Bernard Coupet Alexandre Sukhov

Source: Journal of Mathematical Sciences. 125:825-930

Subject Terms: Lewy-Pinchuk reflection principle, geometry of analytic CR structures, Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables, Global boundary behavior of holomorphic functions of several complex variables, Segre family, Boundary behavior of holomorphic functions of several complex variables, Other notions of convexity in relation to several complex variables, Webster theorem, extension of a biholomorphism, algebraic reflection principle, 01 natural sciences, Fefferman's mapping theorem, Real submanifolds in complex manifolds, geometric reflection principle, topological rigidity of CR mappings, 0101 mathematics, Holomorphically convex complex spaces, reduction theory, deformations of smooth CR structures

File Description: application/xml

Access URL: https://link.springer.com/content/pdf/10.1007/s10958-005-0072-8.pdf
https://link.springer.com/article/10.1007/s10958-005-0072-8
https://rd.springer.com/content/pdf/10.1007%2FPL00021946.pdf

THE RELATION BETWEEN THE SOLID MODULUS OF CONTINUITY AND THE MODULUS OF CONTINUITY ALONG THE SHILOV BOUNDARY FOR ANALYTIC FUNCTIONS OF SEVERAL VARIABLES: Relation between the solid modulus of continuity and modulus of continuity along the Shilov boundary for analytic functions of several variables

Authors: B Ërikke

Source: Mathematics of the USSR-Sbornik. 50:495-511

Subject Terms: maximum principle, continuity modulus function, Global boundary behavior of holomorphic functions of several complex variables, Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube), continuity modulus, regular Weyl region, Boundary behavior of holomorphic functions of several complex variables, Lipschitz condition, Shilov boundary, 0101 mathematics, regular bounded Weil domain, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/3859499
https://ui.adsabs.harvard.edu/abs/1985SbMat..50..495E/abstract

Holomorphic functions with highly noncontinuable boundary behavior

Authors: Edgar Lee Stout Josip Globevnik

Source: Journal d'Analyse Mathématique. 41:211-216

Subject Terms: Global boundary behavior of holomorphic functions of several complex variables, 0103 physical sciences, Pseudoconvex domains, Boundary behavior of holomorphic functions of several complex variables, Continuation of analytic objects in several complex variables, global boundary behavior, strongly pseudoconvex domain, 0101 mathematics, continuation of analytic objects, boundary limit, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/3899268
https://doi.org/10.1007/bf02803401
https://link.springer.com/article/10.1007%2FBF02803401

The holomorphic extension of $C^k$ CR functions on tube submanifolds: The holomorphic extension of \(H^p\)-CR functions on tube submanifolds

Authors: Albert Boggess

Source: Annales Polonici Mathematici. 70:35-42

Subject Terms: Global boundary behavior of holomorphic functions of several complex variables, 4. Education, Extension of functions and other analytic objects from CR manifolds, tube manifold, uniqueness, Bochner's tube theorem, Holomorphic, polynomial and rational approximation, and interpolation in several complex variables, Runge pairs, CR functions, \(H^p\)-CR function, 01 natural sciences, tube manifolds, analytic disc, CR function, holomorphic extension, Real submanifolds in complex manifolds, CR manifolds, 0101 mathematics, approximation, Polynomial convexity, rational convexity, meromorphic convexity in several complex variables

File Description: application/xml

Access URL: https://www.impan.pl/shop/publication/transaction/download/product/110266?download.pdf
https://www.ams.org/proc/1999-127-05/S0002-9939-99-04828-5/S0002-9939-99-04828-5.pdf
https://zbmath.org/1267718
https://doi.org/10.1090/s0002-9939-99-04828-5
https://zbmath.org/1292053
https://doi.org/10.4064/ap-70-1-35-42
https://asu.pure.elsevier.com/en/publications/the-holomorphic-extension-of-hsuppsup-cr-functions-on-tube-subman
https://www.ams.org/proc/1999-127-05/S0002-9939-99-04828-5/S0002-9939-99-04828-5.pdf
https://www.ams.org/journals/proc/1999-127-05/S0002-9939-99-04828-5/home.html
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-apmv70z1p35bwm

One Boundary Version of Morera's Theorem: On a boundary version of Morera's theorem

Authors: S. G. Myslivets

Source: Siberian Mathematical Journal. 42:952-960

Subject Terms: Global boundary behavior of holomorphic functions of several complex variables, boundary Morera theorem, Boundary behavior of holomorphic functions of several complex variables, Continuation of analytic objects in several complex variables, 0102 computer and information sciences, 0101 mathematics, several complex variables, 01 natural sciences, holomorphic continuation, boundary values of a holomorphic function

File Description: application/xml

Access URL: https://zbmath.org/1882364
https://link.springer.com/content/pdf/10.1023/A:1011923929133.pdf
https://eudml.org/doc/50122
https://link.springer.com/article/10.1023%2FA%3A1011923929133

Holomorphic Functions in Tubes Which Have Distributional Boundary Values and Which Are $H^p $ Functions: Holomorphic functions in tubes which have distributional boundary values and which are \(H^ p \)functions

Authors: Richard D. Carmichael Stephen P. Richters

Source: SIAM Journal on Mathematical Analysis. 14:596-621

Subject Terms: \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables, Distributions and ultradistributions as boundary values of analytic functions, holomorphic functions in tubes, Global boundary behavior of holomorphic functions of several complex variables, Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube), distributional boundary values, Boundary behavior of holomorphic functions of several complex variables, Hardy space, 0101 mathematics, Nevanlinna theory, growth estimates, other inequalities of several complex variables, 01 natural sciences

File Description: application/xml

Access URL: https://epubs.siam.org/doi/10.1137/0514047

Boundary uniqueness theorems for analytic functions of several complex variables

Authors: Ehminyan, O. M.

Subject Terms: uniqueness theorem of Bagemihl, Global boundary behavior of holomorphic functions of several complex variables, Boundary value problems in the complex plane, Other generalizations of function theory of one complex variable, boundary behaviour, maximality theorem of Collingwood

File Description: application/xml

Access URL: https://zbmath.org/4044201

Zero-Sets of Continuous Holomorphic Functions on the Boundary of a Strongly Pseudoconvex Domain: Zero-sets of continuous holomorphic functions on the boundary of a strongly pseudoconvex domain

Authors: Barnet M. Weinstock

Source: Journal of the London Mathematical Society. :484-488

Subject Terms: Banach algebras of differentiable or analytic functions, \(H^p\)-spaces, Global boundary behavior of holomorphic functions of several complex variables, interpolation set, Pseudoconvex domains, strongly pseudoconvex domain, peak point, 0101 mathematics, 01 natural sciences, algebra of holomorphic functions, Algebras of holomorphic functions of several complex variables

File Description: application/xml

Access URL: https://zbmath.org/3641835
https://doi.org/10.1112/jlms/s2-18.3.484
https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/jlms/s2-18.3.484

Boundary continuity of some holomorphic functions

Authors: Glicksberg, I.

Source: Pacific J. Math. 80, no. 2 (1979), 425-434

Subject Terms: Banach algebras of continuous functions, function algebras, Banach algebras of differentiable or analytic functions, \(H^p\)-spaces, Global boundary behavior of holomorphic functions of several complex variables, Continuation of analytic objects in several complex variables, 32E35, Shilov boundary, 0101 mathematics, subalgebra of functions, continuous extension, 01 natural sciences, Algebras of holomorphic functions of several complex variables

File Description: application/xml; application/pdf

Access URL: http://msp.org/pjm/1979/80-2/pjm-v80-n2-p13-s.pdf
http://projecteuclid.org/download/pdf_1/euclid.pjm/1102785715
https://projecteuclid.org/euclid.pjm/1102785715
https://msp.org/pjm/1979/80-2/pjm-v80-n2-p13-s.pdf
https://msp.org/pjm/1979/80-2/p13.xhtml
https://projecteuclid.org/download/pdf_1/euclid.pjm/1102785715
http://projecteuclid.org/euclid.pjm/1102785715

Peak sets in real-analytic convex boundaries

Authors: Rachid Belhachemi

Source: Pacific Journal of Mathematics. 185:209-220

Subject Terms: Global boundary behavior of holomorphic functions of several complex variables, holomorphic function, 0101 mathematics, 01 natural sciences, peak set

File Description: application/xml

Access URL: http://msp.org/pjm/1998/185-2/pjm-v185-n2-p02-s.pdf
https://zbmath.org/1344268
https://doi.org/10.2140/pjm.1998.185.209
https://msp.org/pjm/1998/185-2/p02.xhtml
https://msp.org/pjm/1998/185-2/pjm-v185-n2-p02-p.pdf

Invariant metrics and peak functions on pseudoconvex domains of homogeneous finite diagonal type: Invariant metrics and peak functions on pseudoconvex domains of homogeneous finite diagonal type.

Authors: Herbort, Gregor

Source: Mathematische Zeitschrift. 209:223-243

Subject Terms: pseudo-convex domains of homogeneous finite diagonal type, Global boundary behavior of holomorphic functions of several complex variables, Carathéodory-Reiffen metric, Pseudoconvex domains, Carathéodory and Kobayashi pseudodifferential metrics, real-valued plurisubharmonic function, Kobayashi-Royden metric, 01 natural sciences, Article, 510.mathematics, Pluriharmonic and plurisubharmonic functions, peak point, invariant metrics, 0101 mathematics, peak functions, Invariant metrics and pseudodistances in several complex variables, Algebras of holomorphic functions of several complex variables

File Description: application/xml; image/jpeg; application/pdf

Access URL: https://link.springer.com/article/10.1007/BF02570831
https://link.springer.com/content/pdf/10.1007/BF02570831.pdf

A reflection principle for proper holomorphic mappings and geometric invariants

Authors: Faran, James J., V

Source: Mathematische Zeitschrift. 203:363-377

Subject Terms: Proper holomorphic mappings, finiteness theorems, 510.mathematics, boundary regularity, proper holomorphic mappings, Holomorphic mappings and correspondences, Global boundary behavior of holomorphic functions of several complex variables, strictly pseudoconvex domains, 0103 physical sciences, Pseudoconvex domains, reflection principle, 0101 mathematics, 01 natural sciences, Article

File Description: application/xml; image/jpeg; application/pdf

Access URL: https://link.springer.com/article/10.1007%2FBF02570744

Boundary behavior of holomorphic functions on pseudoconvex domains

Authors: Catlin, David

Source: J. Differential Geom. 15, no. 4 (1980), 605-625

Subject Terms: Global boundary behavior of holomorphic functions of several complex variables, Pseudoconvex domains, bounded pseudoconvex domain, Boundary behavior of holomorphic functions of several complex variables, 32E35, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, 01 natural sciences, 32F15, Oka- Weil approximation theorem, 0101 mathematics, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, Levi problem, holomorphic convexity, delta-Neumann problem

File Description: application/xml; application/pdf

Access URL: https://projecteuclid.org/download/pdf_1/euclid.jdg/1214435847
https://projecteuclid.org/journals/journal-of-differential-geometry/volume-15/issue-4/Boundary-behavior-of-holomorphic-functions-on-pseudoconvex-domains/10.4310/jdg/1214435847.full
http://projecteuclid.org/handle/euclid.jdg/1214435847
http://projecteuclid.org/euclid.jdg/1214435847

Condition R and Fefferman′s mapping theorem: Condition \(R\) and Fefferman's mapping theorem

Authors: Patrick W. Darko

Source: International Journal of Mathematics and Mathematical Sciences, Vol 29, Iss 12, Pp 749-752 (2002)

Subject Terms: strictly pseudoconvex manifold, Stein manifold, Global boundary behavior of holomorphic functions of several complex variables, biholomorphic map, QA1-939, Stein spaces, Strongly pseudoconvex domains, 0101 mathematics, Boundary regularity of mappings in several complex variables, 01 natural sciences, Mathematics

File Description: application/xml

Access URL: http://downloads.hindawi.com/journals/ijmms/2002/374790.pdf
https://doaj.org/article/e99feebfe0944115a329190074c83f06
https://www.emis.de/journals/HOA/IJMMS/29/12749.pdf
https://www.hindawi.com/journals/ijmms/2002/374790/
https://downloads.hindawi.com/journals/ijmms/2002/374790.pdf

ZEROS OF HOLOMORPHIC FUNCTIONS OF FINITE ORDER AND WEIGHTED ESTIMATES FOR SOLUTIONS OF THE $\bar\partial$-EQUATION: Zeros of holomorphic functions of finite order and weighted estimates for solutions of the \(\overline\partial\)-equation

Authors: Š A Dautov G M Henkin

Source: Mathematics of the USSR-Sbornik. 35:449-459

Subject Terms: strictly pseudoconvex manifold, Holomorphic functions of several complex variables, Global boundary behavior of holomorphic functions of several complex variables, delta-equation, finite order of growth at the boundary, Pseudoconvex domains, Boundary behavior of holomorphic functions of several complex variables, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, 0101 mathematics, \(\overline\partial\) and \(\overline\partial\)-Neumann operators, 01 natural sciences, zeros of holomorphic functions

File Description: application/xml

Access URL: https://zbmath.org/3654475
https://doi.org/10.1070/sm1979v035n04abeh001551
http://ui.adsabs.harvard.edu/abs/1979SbMat..35..449D/abstract

Some wild holomorphic functions on strictly pseudoconvex domains

Authors: Josip Globevnik

Source: Indagationes Mathematicae (Proceedings). 88:385-396

Subject Terms: boundary behavior of holomorphic function, Global boundary behavior of holomorphic functions of several complex variables, Pseudoconvex domains, Boundary behavior of holomorphic functions of several complex variables, strictly pseudoconvex domain, Continuation of analytic objects in several complex variables, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/3933453
https://www.sciencedirect.com/science/article/pii/138572588590023X