View in EDS

Sharp bounds for singular values of fractional integral operators

Saved in:
Bibliographic Details
Title: Sharp bounds for singular values of fractional integral operators
Authors: Burman, Prabir1 burman@wald.ucdavis.edu
Source: Journal of Mathematical Analysis & Applications. Mar2007, Vol. 327 Issue 1, p251-256. 6p.
Subjects: Integrals, Integral operators, Operator theory, Mathematics
Abstract: Abstract: From the results of Dostanic [M.R. Dostanic, Asymptotic behavior of the singular values of fractional integral operators, J. Math. Anal. Appl. 175 (1993) 380–391] and Vũ and Gorenflo [Kim Tuan Vũ, R. Gorenflo, Singular values of fractional and Volterra integral operators, in: Inverse Problems and Applications to Geophysics, Industry, Medicine and Technology, Ho Chi Minh City, 1995, Ho Chi Minh City Math. Soc., Ho Chi Minh City, 1995, pp. 174–185] it is known that the jth singular value of the fractional integral operator of order is approximately for all large j. In this note we refine this result by obtaining sharp bounds for the singular values and use these bounds to show that the jth singular value is . [Copyright &y& Elsevier]
Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 23161587
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Sharp bounds for singular values of fractional integral operators
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Burman%2C+Prabir%22">Burman, Prabir</searchLink><relatesTo>1</relatesTo><i> burman@wald.ucdavis.edu</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Journal+of+Mathematical+Analysis+%26+Applications%22">Journal of Mathematical Analysis & Applications</searchLink>. Mar2007, Vol. 327 Issue 1, p251-256. 6p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Integrals%22">Integrals</searchLink><br /><searchLink fieldCode="DE" term="%22Integral+operators%22">Integral operators</searchLink><br /><searchLink fieldCode="DE" term="%22Operator+theory%22">Operator theory</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Abstract: From the results of Dostanic [M.R. Dostanic, Asymptotic behavior of the singular values of fractional integral operators, J. Math. Anal. Appl. 175 (1993) 380–391] and Vũ and Gorenflo [Kim Tuan Vũ, R. Gorenflo, Singular values of fractional and Volterra integral operators, in: Inverse Problems and Applications to Geophysics, Industry, Medicine and Technology, Ho Chi Minh City, 1995, Ho Chi Minh City Math. Soc., Ho Chi Minh City, 1995, pp. 174–185] it is known that the jth singular value of the fractional integral operator of order is approximately for all large j. In this note we refine this result by obtaining sharp bounds for the singular values and use these bounds to show that the jth singular value is . [Copyright &y& Elsevier]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=23161587
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.jmaa.2006.03.073
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 6
        StartPage: 251
    Subjects:
      – SubjectFull: Integrals
        Type: general
      – SubjectFull: Integral operators
        Type: general
      – SubjectFull: Operator theory
        Type: general
      – SubjectFull: Mathematics
        Type: general
    Titles:
      – TitleFull: Sharp bounds for singular values of fractional integral operators
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Burman, Prabir
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 03
              Text: Mar2007
              Type: published
              Y: 2007
          Identifiers:
            – Type: issn-print
              Value: 0022247X
          Numbering:
            – Type: volume
              Value: 327
            – Type: issue
              Value: 1
          Titles:
            – TitleFull: Journal of Mathematical Analysis & Applications
              Type: main
ResultId 1