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Matematicheskie Zametki, 2015, Volume 98, Issue 1, Pages 134–146
DOI: https://doi.org/10.4213/mzm10587 (Mi mzm10587) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Regularized Trace of the Dirac Operator

A. O. Shcherbakov

Voronezh State University
Full-text PDF (480 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm10587
Abstract: Formulas for the regularized trace of the one-dimensional non–self-adjoint Dirac operator with L2-potential are obtained. The cases of periodic and antiperiodic boundary conditions as well as of the Dirichlet boundary conditions are considered. The formulas are obtained by using the method of similar operators on the basis of results from the papers [1] and [2].
Keywords: non–self-adjoint Dirac operator, regularized trace, periodic/antiperiodic boundary conditions, Dirichlet boundary conditions, Hilbert space, complex Banach space, Banach algebra, Fourier coefficient.
Funding agency Grant number
Russian Science Foundation 14-21-00066
Russian Foundation for Basic Research 14-01-31196
This work was supported by the Russian Science Foundation under grant 14-21-00066 and by the Russian Foundation for Basic Research under grant 14-01-31196.
Received: 14.10.2014
English version:
Mathematical Notes, 2015, Volume 98, Issue 1, Pages 168–179
DOI: https://doi.org/10.1134/S0001434615070147
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: A. O. Shcherbakov, “Regularized Trace of the Dirac Operator”, Mat. Zametki, 98:1 (2015), 134–146; Math. Notes, 98:1 (2015), 168–179
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    1. A. G. Baskakov, I. A. Krishtal, N. B. Uskova, “O sglazhivanii operatornogo koeffitsienta differentsialnogo operatora pervogo poryadka v banakhovom prostranstve”, Materialy Voronezhskoi mezhdunarodnoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii  i smezhnye problemy», Voronezh, 28 yanvarya – 2 fevralya 2021 g.  Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 206, VINITI RAN, M., 2022, 3–14  mathnet  crossref
    2. César R. de Oliveira, Vinícius L. Rocha, “Bidimensional Honeycomb Materials: A Graph Model Through Dirac Operator”, Reports on Mathematical Physics, 89:2 (2022), 231  crossref
    3. G. V. Garkavenko, N. B. Uskova, “Metod podobnykh operatorov v issledovanii spektralnykh svoistv raznostnykh operatorov s rastuschim potentsialom”, Sib. elektron. matem. izv., 14 (2017), 673–689  mathnet  crossref
    4. I. V. Sadovnichaya, “Equiconvergence of spectral decompositions for the Dirac system with potential in Lebesgue spaces”, Proc. Steklov Inst. Math., 293 (2016), 288–316  mathnet  crossref  crossref  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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