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Matematicheskie Zametki, 2001, Volume 70, Issue 1, Pages 109–122
DOI: https://doi.org/10.4213/mzm724 (Mi mzm724) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Several Formulas for the First Regularized Trace of Discrete Operators

N. G. Tomin

Ivanovo State Textile Academy
Full-text PDF (239 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm724
Abstract: We derive several abstract formulas (of Gelfand–Levitan type) for the first regularized trace of discrete operators under various conditions convenient for verification. The proof of the main result is based on the contour integration method with some modifications from analytic perturbation theory and from the approach proposed earlier by M. Dostani. Some known trace formulas are generalized and improved. We give examples of the applications of our abstract trace formulas for obtaining special trace formulas for ordinary differential operators and for partial differential operators.
Received: 08.10.1999
English version:
Mathematical Notes, 2001, Volume 70, Issue 1, Pages 97–109
DOI: https://doi.org/10.1023/A:1010230103371
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: N. G. Tomin, “Several Formulas for the First Regularized Trace of Discrete Operators”, Mat. Zametki, 70:1 (2001), 109–122; Math. Notes, 70:1 (2001), 97–109
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm724
  • https://doi.org/10.4213/mzm724
  • https://www.mathnet.ru/eng/mzm/v70/i1/p109
    • This publication is cited in the following 3 articles:
    1. N. G. Tomin, I. V. Tomina, “Ob odnoi abstraktnoi formule regulyarizovannykh sledov diskretnykh operatorov i ee primeneniyakh”, Materialy Voronezhskoi vesennei matematicheskoi shkoly «Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya–XXX». Voronezh, 3–9 maya 2019 g. Chast 4, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 193, VINITI RAN, M., 2021, 142–152  mathnet  crossref
    2. Intissar A., “Regularized Trace Formula of Magic Gribov Operator on Bargmann Space”, J. Math. Anal. Appl., 437:1 (2016), 59–70  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Tomin N.G., “K obratnoi zadache spektralnogo analiza dlya odnogo klassa diskretnykh operatorov v gilbertovom prostranstve”, Matematika i ee prilozheniya. zhurnal ivanovskogo matematicheskogo obschestva, 2011, no. 1, 129–138  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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