Zobraziť v EDS

optimal error of analytic continuation from a finite set with inaccurate data in hilbert spaces of holomorphic functions: Optimal error of analytic continuation from a finite set with inaccurate data in Hilbert spaces of holomorphic functions

Uložené v:
Podrobná bibliografia
Názov: optimal error of analytic continuation from a finite set with inaccurate data in hilbert spaces of holomorphic functions: Optimal error of analytic continuation from a finite set with inaccurate data in Hilbert spaces of holomorphic functions
Autori: L. S. Maergoiz, A. M. Fedotov
Zdroj: Siberian Mathematical Journal. 42(5):926-935
Informácie o vydavateľovi: Russian Academy of Sciences - RAS (Rossiĭskaya Akademiya Nauk - RAN), Siberian Branch (Sibirskoe Otdelenie), Sobolev Insitute of Mathematics (Institut Matematiki Im. S. L. Soboleva), Novosibirsk, 2001.
Rok vydania: 2001
Predmety: analytic continuation, Entire functions of several complex variables, Removable singularities in several complex variables, Continuation of analytic objects in several complex variables, extrapolation with inaccurate data, optimal error, optimal linear algorithm
Popis: The article under review refers to the papers [\textit{L.~S.~Maergojz}, Sib. Math. J. 41, No. 6, 1126-1136 (2000; Zbl 0970.32011) and Dokl. Math. 56, No. 2, 674-678 (1997; Zbl 0973.32002)] wherein the problem of optimal extrapolation from a finite set is studied in the class of entire functions with finite spectrum. The aim of the present article is to study this problem in the case of analytic continuation from a finite set with inaccurate data. To estimate the error of a linear functional, an approach is employed suggested by \textit{K.~Miller} in [SIAM J. Math. Anal. 1, 52-74 (1970; Zbl 0214.14804)] based on using the least squares method for ill-posed problems with a prescribed bound. As a result, the authors obtain constructive formulas for calculating the optimal error of the optimal linear algorithm for extrapolation from a set \(U\) to a point \(z_0\) in the class of functions \[ V = \{f\in H(D): \|f\|\leq r\}, \quad r > 0, \] where \(H\) is a Hilbert space with reproducing kernel. Moreover, the asymptotic behavior of the optimal error is investigated in the case when the errors of estimating the initial data tend to zero.
Druh dokumentu: Article
Popis súboru: application/xml
ISSN: 0037-4466
DOI: 10.1023/a:1011967711386
Prístupová URL adresa: https://zbmath.org/1746519
https://link.springer.com/article/10.1023%2FA%3A1011967711386
Prístupové číslo: edsair.dedup.wf.002..a40bceb4194ec2e42a7c72c4b51f7966
Databáza: OpenAIRE
FullText Text:
  Availability: 0
CustomLinks:
  – Url: https://explore.openaire.eu/search/publication?articleId=dedup_wf_002%3A%3Aa40bceb4194ec2e42a7c72c4b51f7966
    Name: EDS - OpenAIRE (s4221598)
    Category: fullText
    Text: View record at OpenAIRE
  – Url: https://resolver.ebscohost.com/openurl?sid=EBSCO:edsair&genre=article&issn=00374466&ISBN=&volume=42&issue=5&date=20010901&spage=926&pages=926-935&title=Siberian Mathematical Journal&atitle=optimal%20error%20of%20analytic%20continuation%20from%20a%20finite%20set%20with%20inaccurate%20data%20in%20hilbert%20spaces%20of%20holomorphic%20functions%3A%20Optimal%20error%20of%20analytic%20continuation%20from%20a%20finite%20set%20with%20inaccurate%20data%20in%20Hilbert%20spaces%20of%20holomorphic%20functions&aulast=L.%20S.%20Maergoiz&id=DOI:10.1023/a:1011967711386
    Name: Full Text Finder
    Category: fullText
    Text: Full Text Finder
    Icon: https://imageserver.ebscohost.com/branding/images/FTF.gif
    MouseOverText: Full Text Finder
  – Url: https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=EBSCO&SrcAuth=EBSCO&DestApp=WOS&ServiceName=TransferToWoS&DestLinkType=GeneralSearchSummary&Func=Links&author=Maergoiz%20LS
    Name: ISI
    Category: fullText
    Text: Nájsť tento článok vo Web of Science
    Icon: https://imagesrvr.epnet.com/ls/20docs.gif
    MouseOverText: Nájsť tento článok vo Web of Science
Header DbId: edsair
DbLabel: OpenAIRE
An: edsair.dedup.wf.002..a40bceb4194ec2e42a7c72c4b51f7966
RelevancyScore: 803
AccessLevel: 3
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 803.185791015625
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: optimal error of analytic continuation from a finite set with inaccurate data in hilbert spaces of holomorphic functions: Optimal error of analytic continuation from a finite set with inaccurate data in Hilbert spaces of holomorphic functions
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22L%2E+S%2E+Maergoiz%22">L. S. Maergoiz</searchLink><br /><searchLink fieldCode="AR" term="%22A%2E+M%2E+Fedotov%22">A. M. Fedotov</searchLink>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <i>Siberian Mathematical Journal</i>. 42(5):926-935
– Name: Publisher
  Label: Publisher Information
  Group: PubInfo
  Data: Russian Academy of Sciences - RAS (Rossiĭskaya Akademiya Nauk - RAN), Siberian Branch (Sibirskoe Otdelenie), Sobolev Insitute of Mathematics (Institut Matematiki Im. S. L. Soboleva), Novosibirsk, 2001.
– Name: DatePubCY
  Label: Publication Year
  Group: Date
  Data: 2001
– Name: Subject
  Label: Subject Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22analytic+continuation%22">analytic continuation</searchLink><br /><searchLink fieldCode="DE" term="%22Entire+functions+of+several+complex+variables%22">Entire functions of several complex variables</searchLink><br /><searchLink fieldCode="DE" term="%22Removable+singularities+in+several+complex+variables%22">Removable singularities in several complex variables</searchLink><br /><searchLink fieldCode="DE" term="%22Continuation+of+analytic+objects+in+several+complex+variables%22">Continuation of analytic objects in several complex variables</searchLink><br /><searchLink fieldCode="DE" term="%22extrapolation+with+inaccurate+data%22">extrapolation with inaccurate data</searchLink><br /><searchLink fieldCode="DE" term="%22optimal+error%22">optimal error</searchLink><br /><searchLink fieldCode="DE" term="%22optimal+linear+algorithm%22">optimal linear algorithm</searchLink>
– Name: Abstract
  Label: Description
  Group: Ab
  Data: The article under review refers to the papers [\textit{L.~S.~Maergojz}, Sib. Math. J. 41, No. 6, 1126-1136 (2000; Zbl 0970.32011) and Dokl. Math. 56, No. 2, 674-678 (1997; Zbl 0973.32002)] wherein the problem of optimal extrapolation from a finite set is studied in the class of entire functions with finite spectrum. The aim of the present article is to study this problem in the case of analytic continuation from a finite set with inaccurate data. To estimate the error of a linear functional, an approach is employed suggested by \textit{K.~Miller} in [SIAM J. Math. Anal. 1, 52-74 (1970; Zbl 0214.14804)] based on using the least squares method for ill-posed problems with a prescribed bound. As a result, the authors obtain constructive formulas for calculating the optimal error of the optimal linear algorithm for extrapolation from a set \(U\) to a point \(z_0\) in the class of functions \[ V = \{f\in H(D): \|f\|\leq r\}, \quad r > 0, \] where \(H\) is a Hilbert space with reproducing kernel. Moreover, the asymptotic behavior of the optimal error is investigated in the case when the errors of estimating the initial data tend to zero.
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Article
– Name: Format
  Label: File Description
  Group: SrcInfo
  Data: application/xml
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0037-4466
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1023/a:1011967711386
– Name: URL
  Label: Access URL
  Group: URL
  Data: <link linkTarget="URL" linkTerm="https://zbmath.org/1746519" linkWindow="_blank">https://zbmath.org/1746519</link><br /><link linkTarget="URL" linkTerm="https://link.springer.com/article/10.1023%2FA%3A1011967711386" linkWindow="_blank">https://link.springer.com/article/10.1023%2FA%3A1011967711386</link>
– Name: AN
  Label: Accession Number
  Group: ID
  Data: edsair.dedup.wf.002..a40bceb4194ec2e42a7c72c4b51f7966
PLink https://erproxy.cvtisr.sk/sfx/access?url=https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsair&AN=edsair.dedup.wf.002..a40bceb4194ec2e42a7c72c4b51f7966
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1023/a:1011967711386
    Languages:
      – Text: Undetermined
    PhysicalDescription:
      Pagination:
        PageCount: 10
        StartPage: 926
    Subjects:
      – SubjectFull: analytic continuation
        Type: general
      – SubjectFull: Entire functions of several complex variables
        Type: general
      – SubjectFull: Removable singularities in several complex variables
        Type: general
      – SubjectFull: Continuation of analytic objects in several complex variables
        Type: general
      – SubjectFull: extrapolation with inaccurate data
        Type: general
      – SubjectFull: optimal error
        Type: general
      – SubjectFull: optimal linear algorithm
        Type: general
    Titles:
      – TitleFull: optimal error of analytic continuation from a finite set with inaccurate data in hilbert spaces of holomorphic functions: Optimal error of analytic continuation from a finite set with inaccurate data in Hilbert spaces of holomorphic functions
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: L. S. Maergoiz
      – PersonEntity:
          Name:
            NameFull: A. M. Fedotov
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 09
              Type: published
              Y: 2001
          Identifiers:
            – Type: issn-print
              Value: 00374466
            – Type: issn-locals
              Value: edsair
          Numbering:
            – Type: volume
              Value: 42
            – Type: issue
              Value: 5
          Titles:
            – TitleFull: Siberian Mathematical Journal
              Type: main
ResultId 1