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TMF, 2008, Volume 157, Number 3, Pages 373–390 (Mi tmf6286)  

This article is cited in 3 scientific papers (total in 3 papers)

Applications of Tauberian theorems in some problems in mathematical physics

Yu. N. Drozhzhinov, B. I. Zavialov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We give some multidimensional Tauberian theorems for generalized functions and show examples of their application in mathematical physics. In particular, we consider the problems of stabilizing the solutions of the Cauchy problem for the heat kernel equation, multicomponent gas diffusion, and the asymptotic Cauchy problem for a free Schrödinger equation in the norms of different Banach spaces among others.

Keywords: Tauberian theorem, generalized function, partial differential equation, holomorphic function, Schrödinger equation, Cauchy problem, Banach space

DOI: https://doi.org/10.4213/tmf6286

Full text: PDF file (486 kB)
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English version:
Theoretical and Mathematical Physics, 2008, 157:3, 1678–1693

Bibliographic databases:

Received: 20.03.2008

Citation: Yu. N. Drozhzhinov, B. I. Zavialov, “Applications of Tauberian theorems in some problems in mathematical physics”, TMF, 157:3 (2008), 373–390; Theoret. and Math. Phys., 157:3 (2008), 1678–1693

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf6286
  • http://mi.mathnet.ru/eng/tmf/v157/i3/p373

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Pilipovic S., Vindas J., “Multidimensional Tauberian Theorems For Vector-Valued Distributions”, Publ. Inst. Math.-Beograd, 95:109 (2014), 1–28  crossref  mathscinet  zmath  isi  scopus
    2. Yu. N. Drozhzhinov, “Multidimensional Tauberian theorems for generalized functions”, Russian Math. Surveys, 71:6 (2016), 1081–1134  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. S. Pilipović, J. Vindas, “Tauberian class estimates for vector-valued distributions”, Sb. Math., 210:2 (2019), 272–296  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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