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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 4, Pages 898–915 (Mi smj1887)  

This article is cited in 10 scientific papers (total in 10 papers)

The Hilbert problem: The case of infinitely many discontinuity points of coefficients

R. B. Salimov, P. L. Shabalin

Kazan State Academy of Architecture and Construction
References:
Abstract: We obtain a solution to the Hilbert boundary value problem in the theory of analytic functions on the half-plane in the case that the coefficients of the boundary condition have countably many discontinuity points of the first kind. We elaborate the two substantially different situations: the series consisting of the jumps of the argument of the coefficient function and the increments of its continuous part converges and this series diverges. Accordingly, Hilbert problems with finite and infinite indices result. We derive formulas for the general solution and investigate the pictures of solvability of these problems.
Keywords: Hilbert boundary value problem, infinite index, entire function, growth indicator function.
Received: 23.01.2007
English version:
Siberian Mathematical Journal, 2008, Volume 49, Issue 4, Pages 718–733
DOI: https://doi.org/10.1007/s11202-008-0069-x
Bibliographic databases:
UDC: 517.54
Language: Russian
Citation: R. B. Salimov, P. L. Shabalin, “The Hilbert problem: The case of infinitely many discontinuity points of coefficients”, Sibirsk. Mat. Zh., 49:4 (2008), 898–915; Siberian Math. J., 49:4 (2008), 718–733
Citation in format AMSBIB
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\by R.~B.~Salimov, P.~L.~Shabalin
\paper The Hilbert problem: The case of infinitely many discontinuity points of coefficients
\jour Sibirsk. Mat. Zh.
\yr 2008
\vol 49
\issue 4
\pages 898--915
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\transl
\jour Siberian Math. J.
\yr 2008
\vol 49
\issue 4
\pages 718--733
\crossref{https://doi.org/10.1007/s11202-008-0069-x}
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  • https://www.mathnet.ru/eng/smj/v49/i4/p898
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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