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Izvestiya: Mathematics, 2003, Volume 67, Issue 1, Pages 161–181
DOI: https://doi.org/10.1070/IM2003v067n01ABEH000423
(Mi im423)
 

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

Tangential boundary values of Laplace transforms. Applications to Muntz–Szasz type approximation

A. M. Sedletskii

M. V. Lomonosov Moscow State University
References:
Abstract: We consider the Laplace transforms (LT) of functions in $L^q(\mathbb R_+)$, $1<q\leqslant 2$, with a slowly varying weight. We prove that if the weight satisfies certain conditions, then each LT of this class has tangential boundary values almost everywhere on the imaginary axis, and the structure of the corresponding neighbourhoods depends on the weight only. This result is applied to distinguish a wide class of weighted $L^p$ spaces on the half-line such that the Szasz condition is not necessary for the completeness of the system $\exp(-\lambda_n t)$ in these spaces.
Received: 28.02.2002
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2003, Volume 67, Issue 1, Pages 177–198
DOI: https://doi.org/10.4213/im423
Bibliographic databases:
UDC: 517.5
MSC: 30D40, 41A30
Language: English
Original paper language: Russian
Citation: A. M. Sedletskii, “Tangential boundary values of Laplace transforms. Applications to Muntz–Szasz type approximation”, Izv. RAN. Ser. Mat., 67:1 (2003), 177–198; Izv. Math., 67:1 (2003), 161–181
Citation in format AMSBIB
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\by A.~M.~Sedletskii
\paper Tangential boundary values of Laplace transforms. Applications to Muntz--Szasz type approximation
\jour Izv. RAN. Ser. Mat.
\yr 2003
\vol 67
\issue 1
\pages 177--198
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\transl
\jour Izv. Math.
\yr 2003
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\pages 161--181
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Linking options:
  • https://www.mathnet.ru/eng/im423
  • https://doi.org/10.1070/IM2003v067n01ABEH000423
  • https://www.mathnet.ru/eng/im/v67/i1/p177
  • 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
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:490
    Russian version PDF:209
    English version PDF:22
    References:78
    First page:1
     
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