Sobolev, AV;
(2017)
Functions of self-adjoint operators in ideals of compact operators.
Journal of the London Mathematical Society
, 95
(1)
pp. 157-176.
10.1112/jlms.12010.
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Abstract
For self-adjoint operators A,B, a bounded operator J, and a function f:R→C, we obtain bounds in quasi-normed ideals of compact operators for the difference f(A)J−Jf(B) in terms of the operator AJ−JB. The focus is on functions f that are smooth everywhere except for finitely many points. A typical example is the function f(t)=|t|γ with γ∈(0,1). The obtained results are applied to derive a two-term quasi-classical asymptotic formula for the trace trf(S) with S being a Wiener–Hopf operator with a discontinuous symbol.
| Type: | Article |
|---|---|
| Title: | Functions of self-adjoint operators in ideals of compact operators |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1112/jlms.12010 |
| Publisher version: | https://doi.org/10.1112/jlms.12010 |
| Language: | English |
| Additional information: | © 2017 The Authors. The Journal of the London Mathematical Society is copyright © London Mathematical Society. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. |
| Keywords: | 47G30; 47B15 (primary); 45M05; 35S05; 47B10; 47B35 (secondary) |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1537577 |
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