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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

Hill discriminants and spectra of periodic Jacobi matrices


Author: V. A. Marchenko
Translated by: the author
Original publication: Algebra i Analiz, tom 25 (2013), nomer 2.
Journal: St. Petersburg Math. J. 25 (2014), 265-269
MSC (2010): Primary 47B36
DOI: https://doi.org/10.1090/S1061-0022-2014-01289-7
Published electronically: March 12, 2014
MathSciNet review: 3114852
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Abstract | References | Similar Articles | Additional Information

Abstract: The spectra of periodic Jacobi matrices are described completely without use of conformal mappings.


References [Enhancements On Off] (What's this?)

  • 1. V. A. Marčenko and I. V. Ostrovs'kiĭ, A characterization of the spectrum of the Hill operator, Mat. Sb. (N.S.) 97 (1975), no. 4, 540-606, 633-634. (Russian) MR 0409965 (53:13717)
  • 2. L. V. Perkolab, An inverse problem for a periodic Sacobi matrix, Teor. Funktsĭi Funktional. Anal. i Priložen. 42 (1984), 107-121. (Russian) MR 751397 (86j:47036)

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Additional Information

V. A. Marchenko
Affiliation: Mathematics Department, B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Science of Ukraine, Lenin av. 47, Kharkov 61103, Ukraine
Email: Marchenko@ilt.kharkov.ua

DOI: https://doi.org/10.1090/S1061-0022-2014-01289-7
Keywords: Hill discriminants, spectra of periodic Jacobi matrices
Received by editor(s): November 5, 2012
Published electronically: March 12, 2014
Dedicated: In memory of Vladimir Savel’evich Buslaev
Article copyright: © Copyright 2014 American Mathematical Society

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