Estimates For Fractional Powers And Logarithm Of Operators With Hilbert-Schmidt Resolvents And Perturbation Results

Michael Gil

doi:10.12732/ijam.v34i4.1

Estimates For Fractional Powers And Logarithm Of Operators With Hilbert-Schmidt Resolvents And Perturbation Results

Michael Gil

Department of Mathematics

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

1 Scopus citations

Abstract

Let A be a closed operator on a separable Hilbert space with the spectrum in the open right half-plane and a bounded Hermitian component, and let the resolvent of A be a Hilbert-Schmidt operator. The paper deals with the function (formula presented) where µ is a nondecreasing function and I is the unit operator. We establish norm estimates and perturbations results for hµ(A). As particular cases the fractional powers and logarithm of A are considered.

Original language	English
Pages (from-to)	607-620
Number of pages	14
Journal	International Journal of Applied Mathematics
Volume	34
Issue number	4
DOIs	https://doi.org/10.12732/ijam.v34i4.1
State	Published - 1 Jan 2021

Keywords

Hilbert space
fractional power of operators
operator logarithm Hirsch type functions
perturbations

ASJC Scopus subject areas

General Mathematics
Computational Theory and Mathematics

Access to Document

10.12732/ijam.v34i4.1

Cite this

@article{2195fd30ab0b4e288cf6d764a7ed93f2,

title = "Estimates For Fractional Powers And Logarithm Of Operators With Hilbert-Schmidt Resolvents And Perturbation Results",

abstract = "Let A be a closed operator on a separable Hilbert space with the spectrum in the open right half-plane and a bounded Hermitian component, and let the resolvent of A be a Hilbert-Schmidt operator. The paper deals with the function (formula presented) where µ is a nondecreasing function and I is the unit operator. We establish norm estimates and perturbations results for hµ(A). As particular cases the fractional powers and logarithm of A are considered.",

keywords = "Hilbert space, fractional power of operators, operator logarithm Hirsch type functions, perturbations",

author = "Michael Gil",

year = "2021",

month = jan,

day = "1",

doi = "10.12732/ijam.v34i4.1",

language = "English",

volume = "34",

pages = "607--620",

journal = "International Journal of Applied Mathematics",

issn = "1311-1728",

publisher = "Diogenes Co. Ltd.",

number = "4",

}

TY - JOUR

T1 - Estimates For Fractional Powers And Logarithm Of Operators With Hilbert-Schmidt Resolvents And Perturbation Results

AU - Gil, Michael

PY - 2021/1/1

Y1 - 2021/1/1

N2 - Let A be a closed operator on a separable Hilbert space with the spectrum in the open right half-plane and a bounded Hermitian component, and let the resolvent of A be a Hilbert-Schmidt operator. The paper deals with the function (formula presented) where µ is a nondecreasing function and I is the unit operator. We establish norm estimates and perturbations results for hµ(A). As particular cases the fractional powers and logarithm of A are considered.

AB - Let A be a closed operator on a separable Hilbert space with the spectrum in the open right half-plane and a bounded Hermitian component, and let the resolvent of A be a Hilbert-Schmidt operator. The paper deals with the function (formula presented) where µ is a nondecreasing function and I is the unit operator. We establish norm estimates and perturbations results for hµ(A). As particular cases the fractional powers and logarithm of A are considered.

KW - Hilbert space

KW - fractional power of operators

KW - operator logarithm Hirsch type functions

KW - perturbations

UR - https://www.scopus.com/pages/publications/85118715889

U2 - 10.12732/ijam.v34i4.1

DO - 10.12732/ijam.v34i4.1

M3 - Article

AN - SCOPUS:85118715889

SN - 1311-1728

VL - 34

SP - 607

EP - 620

JO - International Journal of Applied Mathematics

JF - International Journal of Applied Mathematics

IS - 4

ER -

Estimates For Fractional Powers And Logarithm Of Operators With Hilbert-Schmidt Resolvents And Perturbation Results

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this