Asymptotics of singular values of fractional integral operators

Vu Kim Tuan; R. Gorenflo

doi:10.1088/0266-5611/10/4/013

Asymptotics of singular values of fractional integral operators

Vu Kim Tuan^*
, R. Gorenflo

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

The singular values sigma _n of the fractional integral operator (x^{- beta}I₀^alphau)(x)=x^{- beta} integral ₀^x((x-t)^{alpha -1})/( Gamma ( alpha ))u(t)dt, 0<x<1, alpha >2 beta >or=0, in L₂(0,1) are proved to have the asymptotics sigma _n approximately=n ^{- alpha} as n to infinity .

Original language	English
Article number	013
Pages (from-to)	949-955
Number of pages	7
Journal	Inverse Problems
Volume	10
Issue number	4
DOIs	https://doi.org/10.1088/0266-5611/10/4/013
State	Published - 1994

ASJC Scopus subject areas

Theoretical Computer Science
Signal Processing
Mathematical Physics
Computer Science Applications
Applied Mathematics

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title = "Asymptotics of singular values of fractional integral operators",

abstract = "The singular values sigma n of the fractional integral operator (x- betaI0alphau)(x)=x- beta integral 0x((x-t)alpha -1)/( Gamma ( alpha ))u(t)dt, 02 beta >or=0, in L2(0,1) are proved to have the asymptotics sigma n approximately=n - alpha as n to infinity .",

author = "Tuan, \{Vu Kim\} and R. Gorenflo",

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doi = "10.1088/0266-5611/10/4/013",

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T1 - Asymptotics of singular values of fractional integral operators

AU - Tuan, Vu Kim

AU - Gorenflo, R.

PY - 1994

Y1 - 1994

N2 - The singular values sigma n of the fractional integral operator (x- betaI0alphau)(x)=x- beta integral 0x((x-t)alpha -1)/( Gamma ( alpha ))u(t)dt, 02 beta >or=0, in L2(0,1) are proved to have the asymptotics sigma n approximately=n - alpha as n to infinity .

AB - The singular values sigma n of the fractional integral operator (x- betaI0alphau)(x)=x- beta integral 0x((x-t)alpha -1)/( Gamma ( alpha ))u(t)dt, 02 beta >or=0, in L2(0,1) are proved to have the asymptotics sigma n approximately=n - alpha as n to infinity .

UR - https://www.scopus.com/pages/publications/0347348344

U2 - 10.1088/0266-5611/10/4/013

DO - 10.1088/0266-5611/10/4/013

M3 - Article

AN - SCOPUS:0347348344

SN - 0266-5611

VL - 10

SP - 949

EP - 955

JO - Inverse Problems

JF - Inverse Problems

IS - 4

M1 - 013

ER -

Asymptotics of singular values of fractional integral operators

Abstract

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