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Funktsional'nyi Analiz i ego Prilozheniya, 2006, Volume 40, Issue 4, Pages 33–48
DOI: https://doi.org/10.4213/faa852 (Mi faa852) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On Functions Uniquely Determined by Their Asymptotic Expansion

V. P. Gurariia, D. W. H. Gillamb

a Monash University
b Swinburne University of Technology
Full-text PDF (278 kB) Citations (3)
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DOI: https://doi.org/10.4213/faa852
Abstract: We present a maximal class of analytic functions. The elements of this class are uniquely determined by their asymptotic expansions. We also discuss the possibility of recovery of a function from the coefficients of its asymptotic series. In particular, we consider the problem of recovering by using Borel summation. The last published result in this direction was obtained by Alan Sokal in 1980, but his paper well known to physicists (in quantum field theory) seems to have remained unnoticed by mathematicians.
Keywords: Watson's uniqueness theorem, Gevrey expansions, Laplace transforms in complex domain, differential equations in complex domain.
Received: 07.04.2006
English version:
Functional Analysis and Its Applications, 2006, Volume 40, Issue 4, Pages 273–284
DOI: https://doi.org/10.1007/s10688-006-0044-x
Bibliographic databases:
Document Type: Article
UDC: 517.53+517.928
Language: Russian
Citation: V. P. Gurarii, D. W. H. Gillam, “On Functions Uniquely Determined by Their Asymptotic Expansion”, Funktsional. Anal. i Prilozhen., 40:4 (2006), 33–48; Funct. Anal. Appl., 40:4 (2006), 273–284
Citation in format AMSBIB
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    • This publication is cited in the following 3 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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    References:47
    First page:3
     
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