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Mat. Zametki, 2017, Volume 102, Issue 2, Pages 197–215 (Mi mz11430)  

This article is cited in 1 scientific paper (total in 1 paper)

Trace of Order $(-1)$ for a String with Singular Weight

A. S. Ivanov, A. M. Savchuk

Lomonosov Moscow State University

Abstract: The Sturm–Liouville problem on a finite closed interval with potential and weight of first order of singularity is studied. Estimates for the $s$-numbers and eigenvalues of the corresponding integral operator are obtained. The spectral trace of first negative order is evaluated in terms of the integral kernel. The obtained theoretical results are illustrated by examples.

Keywords: spectral asymptotics, Sturm–Liouville problem, spectral trace.

Funding Agency Grant Number
Russian Science Foundation 14-01-00754
This work was supported by the Russian Science Foundation under grant 14-01-00754.


DOI: https://doi.org/10.4213/mzm11430

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English version:
Mathematical Notes, 2017, 102:2, 164–180

Bibliographic databases:

Document Type: Article
UDC: 517.927.2
Received: 31.10.2016
Revised: 01.02.2017

Citation: A. S. Ivanov, A. M. Savchuk, “Trace of Order $(-1)$ for a String with Singular Weight”, Mat. Zametki, 102:2 (2017), 197–215; Math. Notes, 102:2 (2017), 164–180

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/mz11430
  • https://doi.org/10.4213/mzm11430
  • http://mi.mathnet.ru/eng/mz/v102/i2/p197

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. S. Ivanov, “Traces of higher negative orders for a string with a singular weight”, Differ. Equ., 54:10 (2018), 1310–1320  crossref  crossref  mathscinet  zmath  isi  elib  scopus
  • Математические заметки Mathematical Notes
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