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Izv. RAN. Ser. Mat., 2003, Volume 67, Issue 1, Pages 177–198 (Mi izv423)  

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

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.

DOI: https://doi.org/10.4213/im423

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English version:
Izvestiya: Mathematics, 2003, 67:1, 161–181

Bibliographic databases:

UDC: 517.5
MSC: 30D40, 41A30
Received: 28.02.2002

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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\pages 177--198
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\pages 161--181
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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. A. M. Sedletskii, “Analytic Fourier Transforms and Exponential Approximations. II”, Journal of Mathematical Sciences, 130:6 (2005), 5083–5255  mathnet  crossref  mathscinet  zmath
    2. A. M. Sedletskii, “Müntz–Szász type approximation in direct products of spaces”, Izv. Math., 70:5 (2006), 1031–1050  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. V. G. Krotov, L. V. Smovzh, “Weighted estimates for tangential boundary behaviour”, Sb. Math., 197:2 (2006), 193–211  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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