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Trace formulae for perturbations of class Sm. / Peller, V. V.; Александров, Алексей Борисович.

в: Journal of Spectral Theory, Том 1, № 1, 2011, стр. 1-26.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Peller, VV & Александров, АБ 2011, 'Trace formulae for perturbations of class Sm', Journal of Spectral Theory, Том. 1, № 1, стр. 1-26. https://doi.org/10.4171/JST/1

APA

Peller, V. V., & Александров, А. Б. (2011). Trace formulae for perturbations of class Sm. Journal of Spectral Theory, 1(1), 1-26. https://doi.org/10.4171/JST/1

Vancouver

Peller VV, Александров АБ. Trace formulae for perturbations of class Sm. Journal of Spectral Theory. 2011;1(1):1-26. https://doi.org/10.4171/JST/1

Author

Peller, V. V. ; Александров, Алексей Борисович. / Trace formulae for perturbations of class Sm. в: Journal of Spectral Theory. 2011 ; Том 1, № 1. стр. 1-26.

BibTeX

@article{9d653225ec93473bbc3a05cc4de80915,
title = "Trace formulae for perturbations of class Sm",
abstract = "We obtain general trace formulae in the case of perturbation of self-adjoint operators by self-adjoint operators of class Sm, where m is a positive integer. In [25] a trace formula for operator Taylor polynomials was obtained. This formula includes the Lifshits-Krein trace formula in the case m = 1 and the Koplienko trace formula in the case m = 2. We establish most general trace formulae in the case of perturbation of Schatten-von Neumann class Sm. We also improve the trace formula obtained in [25] for operator Taylor polynomials and prove it for arbitrary functions in the Besov space B∞1m(R). We consider several other special cases of our general trace formulae. In particular, we establish a trace formula for m-th order operator differences.",
keywords = "Besov spaces, Multiple operator integrals, Perturbation, Schatten-von Neumann classes, Trace formulae",
author = "Peller, {V. V.} and Александров, {Алексей Борисович}",
note = "Publisher Copyright: {\textcopyright} European Mathematical Society.",
year = "2011",
doi = "10.4171/JST/1",
language = "English",
volume = "1",
pages = "1--26",
journal = "Journal of Spectral Theory",
issn = "1664-039X",
publisher = "European Mathematical Society Publishing House",
number = "1",

}

RIS

TY - JOUR

T1 - Trace formulae for perturbations of class Sm

AU - Peller, V. V.

AU - Александров, Алексей Борисович

N1 - Publisher Copyright: © European Mathematical Society.

PY - 2011

Y1 - 2011

N2 - We obtain general trace formulae in the case of perturbation of self-adjoint operators by self-adjoint operators of class Sm, where m is a positive integer. In [25] a trace formula for operator Taylor polynomials was obtained. This formula includes the Lifshits-Krein trace formula in the case m = 1 and the Koplienko trace formula in the case m = 2. We establish most general trace formulae in the case of perturbation of Schatten-von Neumann class Sm. We also improve the trace formula obtained in [25] for operator Taylor polynomials and prove it for arbitrary functions in the Besov space B∞1m(R). We consider several other special cases of our general trace formulae. In particular, we establish a trace formula for m-th order operator differences.

AB - We obtain general trace formulae in the case of perturbation of self-adjoint operators by self-adjoint operators of class Sm, where m is a positive integer. In [25] a trace formula for operator Taylor polynomials was obtained. This formula includes the Lifshits-Krein trace formula in the case m = 1 and the Koplienko trace formula in the case m = 2. We establish most general trace formulae in the case of perturbation of Schatten-von Neumann class Sm. We also improve the trace formula obtained in [25] for operator Taylor polynomials and prove it for arbitrary functions in the Besov space B∞1m(R). We consider several other special cases of our general trace formulae. In particular, we establish a trace formula for m-th order operator differences.

KW - Besov spaces

KW - Multiple operator integrals

KW - Perturbation

KW - Schatten-von Neumann classes

KW - Trace formulae

UR - http://www.scopus.com/inward/record.url?scp=84994076454&partnerID=8YFLogxK

U2 - 10.4171/JST/1

DO - 10.4171/JST/1

M3 - Article

AN - SCOPUS:84994076454

VL - 1

SP - 1

EP - 26

JO - Journal of Spectral Theory

JF - Journal of Spectral Theory

SN - 1664-039X

IS - 1

ER -

ID: 87317612