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Matematicheskie Zametki, 2022, Volume 111, Issue 3, Pages 339–353
DOI: https://doi.org/10.4213/mzm13310
(Mi mzm13310)
 

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

On the Uniform Stability of Recovering Sine-Type Functions with Asymptotically Separated Zeros

S. A. Buterin

Saratov State University
References:
Abstract: We obtain the uniform stability of recovering entire functions of special form from their zeros. To such a form, we can reduce the characteristic determinants of strongly regular differential operators and pencils of the first and the second orders, including differential systems with asymptotically separated eigenvalues whose characteristic numbers lie on a line containing the origin, as well as the nonlocal perturbations of these operators. We prove that the dependence of such functions on the sequences of their zeros is Lipschitz continuous with respect to natural metrics on each ball of a finite radius. Results of this type can be used for studying the uniform stability of inverse spectral problems. In addition, general theorems on the asymptotics of zeros of functions of this class and on their equivalent representation via an infinite product are obtained, which give the corresponding results for many specific operators.
Keywords: sine-type function, strongly regular differential operator, eigenvalues, characteristic determinant, infinite product, uniform stability, Lipschitz stability.
Funding agency Grant number
Russian Foundation for Basic Research 20-31-70005
This work was supported by the Russian Foundation for Basic Research under grant 20-31-70005.
Received: 28.09.2021
English version:
Mathematical Notes, 2022, Volume 111, Issue 3, Pages 343–355
DOI: https://doi.org/10.1134/S0001434622030026
Bibliographic databases:
Document Type: Article
UDC: 517.984
Language: Russian
Citation: S. A. Buterin, “On the Uniform Stability of Recovering Sine-Type Functions with Asymptotically Separated Zeros”, Mat. Zametki, 111:3 (2022), 339–353; Math. Notes, 111:3 (2022), 343–355
Citation in format AMSBIB
\Bibitem{But22}
\by S.~A.~Buterin
\paper On the Uniform Stability of Recovering Sine-Type Functions with Asymptotically Separated Zeros
\jour Mat. Zametki
\yr 2022
\vol 111
\issue 3
\pages 339--353
\mathnet{http://mi.mathnet.ru/mzm13310}
\crossref{https://doi.org/10.4213/mzm13310}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4461265}
\transl
\jour Math. Notes
\yr 2022
\vol 111
\issue 3
\pages 343--355
\crossref{https://doi.org/10.1134/S0001434622030026}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85123704215}
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  • https://www.mathnet.ru/eng/mzm13310
  • https://doi.org/10.4213/mzm13310
  • https://www.mathnet.ru/eng/mzm/v111/i3/p339
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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