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Mat. Zametki, 1978, Volume 23, Issue 2, Pages 237–248 (Mi mz8137)  

This article is cited in 6 scientific papers (total in 6 papers)

Determination of an infinite non-self-adjoint Jacobi matrix from its generalized spectral function

G. Sh. Guseinov

M. V. Lomonosov Moscow State University

Abstract: Restoration from the generalized spectral function of the equations
\begin{gather*} b_0y_0+a_0y_1=\lambda y_2,
a_{n-1}y_{n-1}+b_ny_n+a_ny_{n+1}=\lambda y_n,\quad n=1,2,3,…, \end{gather*}
where $a_n$ and $b_n$ are arbitrary complex numbers, $a_n\ne0$ ($n=0,1,2,…$), $\lambda$ is a complex parameter, and $\{y_n\}_0^\infty$ infin is the required solution, is investigated. Necessary and sufficient conditions for solvability of the inverse problem are obtained, and the restoration procedure is described.

Full text: PDF file (795 kB)

English version:
Mathematical Notes, 1978, 23:2, 130–136

Bibliographic databases:

UDC: 517.9
Received: 22.12.1976

Citation: G. Sh. Guseinov, “Determination of an infinite non-self-adjoint Jacobi matrix from its generalized spectral function”, Mat. Zametki, 23:2 (1978), 237–248; Math. Notes, 23:2 (1978), 130–136

Citation in format AMSBIB
\Bibitem{Gus78}
\by G.~Sh.~Guseinov
\paper Determination of an infinite non-self-adjoint Jacobi matrix from its generalized spectral function
\jour Mat. Zametki
\yr 1978
\vol 23
\issue 2
\pages 237--248
\mathnet{http://mi.mathnet.ru/mz8137}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=485911}
\zmath{https://zbmath.org/?q=an:0428.47017|0413.47015}
\transl
\jour Math. Notes
\yr 1978
\vol 23
\issue 2
\pages 130--136
\crossref{https://doi.org/10.1007/BF01153153}


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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. M. M. Gekhtman, “Integration of non-Abelian Toda-type chains”, Funct. Anal. Appl., 24:3 (1990), 231–233  mathnet  crossref  mathscinet  zmath  isi
    2. A. S. Osipov, “O determinantnom kriterii slabosovershennosti sistem funktsii, golomorfnykh v beskonechnosti, i ikh svyazi s nekotorymi klassami raznostnykh operatorov vysokogo poryadka”, Fundament. i prikl. matem., 1:3 (1995), 711–727  mathnet  mathscinet  zmath
    3. V. A. Yurko, “On discrete operators of higher order”, Russian Math. Surveys, 51:3 (1996), 578–580  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. Gusein Sh. Guseinov, “Inverse Spectral Problems for Tridiagonal $N$ by $N$ Complex Hamiltonians”, SIGMA, 5 (2009), 018, 28 pp.  mathnet  crossref  mathscinet  zmath
    5. Sergey M. Zagorodnyuk, “On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum”, SIGMA, 7 (2011), 016, 9 pp.  mathnet  crossref  mathscinet
    6. V. A. Yurko, “Obratnaya spektralnaya zadacha dlya diskretnykh operatorov v topologicheskikh prostranstvakh”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:4(1) (2014), 439–447  mathnet  crossref  elib
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