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Kato smoothness and functions of perturbed self-adjoint operators

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Kato smoothness and functions of perturbed self-adjoint operators. / Frank, Rupert L.; Pushnitski, Alexander.

In: ADVANCES IN MATHEMATICS, Vol. 351, 31.07.2019, p. 343-387.

Research output: Contribution to journalArticle

Harvard

Frank, RL & Pushnitski, A 2019, 'Kato smoothness and functions of perturbed self-adjoint operators', ADVANCES IN MATHEMATICS, vol. 351, pp. 343-387. https://doi.org/10.1016/j.aim.2019.05.002

APA

Frank, R. L., & Pushnitski, A. (2019). Kato smoothness and functions of perturbed self-adjoint operators. ADVANCES IN MATHEMATICS, 351, 343-387. https://doi.org/10.1016/j.aim.2019.05.002

Vancouver

Frank RL, Pushnitski A. Kato smoothness and functions of perturbed self-adjoint operators. ADVANCES IN MATHEMATICS. 2019 Jul 31;351:343-387. https://doi.org/10.1016/j.aim.2019.05.002

Author

Frank, Rupert L. ; Pushnitski, Alexander. / Kato smoothness and functions of perturbed self-adjoint operators. In: ADVANCES IN MATHEMATICS. 2019 ; Vol. 351. pp. 343-387.

Bibtex Download

@article{b51839d1d9df48f99ea3cb42ae0a1d12,
title = "Kato smoothness and functions of perturbed self-adjoint operators",
abstract = "We consider the difference f(H1) - f(H0) for self-adjoint operators H0 and H1 acting in a Hilbert space. We establish a new class of estimates for the operator norm and the Schatten class norms of this difference. Our estimates utilise ideas of scattering theory and involve conditions on H0  and H1  in terms of the Kato smoothness. They allow for a much wider class of functions f (including some unbounded ones) than previously available results. As an important technical tool, we propose a new notion of Schatten class valued smoothness and develop a new framework for double operator integrals.",
keywords = "Double operator integrals, Kato smoothness, Schatten classes",
author = "Frank, {Rupert L.} and Alexander Pushnitski",
year = "2019",
month = jul,
day = "31",
doi = "10.1016/j.aim.2019.05.002",
language = "English",
volume = "351",
pages = "343--387",
journal = "ADVANCES IN MATHEMATICS",
issn = "0001-8708",
publisher = "ACADEMIC PRESS INC",

}

RIS (suitable for import to EndNote) Download

TY - JOUR

T1 - Kato smoothness and functions of perturbed self-adjoint operators

AU - Frank, Rupert L.

AU - Pushnitski, Alexander

PY - 2019/7/31

Y1 - 2019/7/31

N2 - We consider the difference f(H1) - f(H0) for self-adjoint operators H0 and H1 acting in a Hilbert space. We establish a new class of estimates for the operator norm and the Schatten class norms of this difference. Our estimates utilise ideas of scattering theory and involve conditions on H0  and H1  in terms of the Kato smoothness. They allow for a much wider class of functions f (including some unbounded ones) than previously available results. As an important technical tool, we propose a new notion of Schatten class valued smoothness and develop a new framework for double operator integrals.

AB - We consider the difference f(H1) - f(H0) for self-adjoint operators H0 and H1 acting in a Hilbert space. We establish a new class of estimates for the operator norm and the Schatten class norms of this difference. Our estimates utilise ideas of scattering theory and involve conditions on H0  and H1  in terms of the Kato smoothness. They allow for a much wider class of functions f (including some unbounded ones) than previously available results. As an important technical tool, we propose a new notion of Schatten class valued smoothness and develop a new framework for double operator integrals.

KW - Double operator integrals

KW - Kato smoothness

KW - Schatten classes

UR - http://www.scopus.com/inward/record.url?scp=85065795990&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2019.05.002

DO - 10.1016/j.aim.2019.05.002

M3 - Article

VL - 351

SP - 343

EP - 387

JO - ADVANCES IN MATHEMATICS

JF - ADVANCES IN MATHEMATICS

SN - 0001-8708

ER -

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