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Funktsional'nyi Analiz i ego Prilozheniya, 2009, Volume 43, Issue 3, Pages 26–32
DOI: https://doi.org/10.4213/faa2958 (Mi faa2958) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Two-Sided Estimates for the Trace of the Difference of Two Semigroups

M. Sh. Birman, V. A. Sloushch

St. Petersburg State University, Faculty of Physics
Full-text PDF (178 kB) Citations (4)
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DOI: https://doi.org/10.4213/faa2958
Abstract: This paper deals with the derivation of two-sided estimates for the trace of the difference of two semigroups generated by two Schrödinger operators in $L_{2}(\mathbb{R}^{3})$ with trace class difference of the resolvents. Use is made of a purely operator-theoretic technique. The results are stated in a rather general abstract form. The sharpness of our estimates is confirmed by the fact that they imply the asymptotic behavior of the trace of the difference of the semigroups as $t\to+0$. Our considerations are substantially based on the Krein–Lifshits formula and on the Birman–Solomyak representation for the spectral shift function.
Keywords: spectral shift function, Schrödinger operator, trace formula.
Received: 18.02.2009
English version:
Functional Analysis and Its Applications, 2009, Volume 43, Issue 3, Pages 184–189
DOI: https://doi.org/10.1007/s10688-009-0026-x
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: M. Sh. Birman, V. A. Sloushch, “Two-Sided Estimates for the Trace of the Difference of Two Semigroups”, Funktsional. Anal. i Prilozhen., 43:3 (2009), 26–32; Funct. Anal. Appl., 43:3 (2009), 184–189
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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