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Zapiski Nauchnykh Seminarov POMI, 1999, Volume 262, Pages 147–171 (Mi znsl1110)  
This article is cited in 10 scientific papers (total in 10 papers)

Inclusion of Hamburger's power moment problem in the spectral theory of the canonical systems

I. S. Kats

Odessa State Academy of Food Technology
Full-text PDF (288 kB) Citations (10)
Abstract: Hamburger's power moment problem (shortly HPMP) that has a solution with infinitely many points of increase is shown to be the problem of finding all spectral functions for some canonical system of the linear differential equations of phase dimension 2 and with Hamiltonian of special class. A rule for construction of this Hamiltonian using the data of HPMP is given. In this connection the Hamburger criterion for the uniqueness of a solution of HPMP acquires a “natural form”, and some results of the classical HPMP theory receive simple proofs.
Received: 04.04.1999
English version:
Journal of Mathematical Sciences (New York), 2002, Volume 110, Issue 5, Pages 2991–3004
DOI: https://doi.org/10.1023/A:1015391405016
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: I. S. Kats, “Inclusion of Hamburger's power moment problem in the spectral theory of the canonical systems”, Investigations on linear operators and function theory. Part 27, Zap. Nauchn. Sem. POMI, 262, POMI, St. Petersburg, 1999, 147–171; J. Math. Sci. (New York), 110:5 (2002), 2991–3004
Citation in format AMSBIB
\Bibitem{Kat99}
\by I.~S.~Kats
\paper Inclusion of Hamburger's power moment problem in the spectral theory of the canonical systems
\inbook Investigations on linear operators and function theory. Part~27
\serial Zap. Nauchn. Sem. POMI
\yr 1999
\vol 262
\pages 147--171
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1110}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1734332}
\zmath{https://zbmath.org/?q=an:1005.44004}
\transl
\jour J. Math. Sci. (New York)
\yr 2002
\vol 110
\issue 5
\pages 2991--3004
\crossref{https://doi.org/10.1023/A:1015391405016}
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    • 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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