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On a generalization of the three spectral inverse problem

O. P. Boyko, O. M. Martynyuk, V. N. Pivovarchik
arXiv:1609.02955      Article (.pdf)

Abstract

We consider a generalization of the three spectral inverse problem, that is, for given spectrum of the Dirichlet-Dirichlet problem (the Sturm-Liouville problem with Dirichlet conditions at both ends) on the whole interval $[0,a]$, parts of spectra of the Dirichlet-Neumann and Dirichlet-Dirichlet problems on $[0,a/2]$ and parts of spectra of the Dirichlet-Newman and Dirichlet-Dirichlet problems on $[a/2,a]$, we find the potential of the Sturm-Liouville equation.

Key words: Sturm-Liouville equation, Dirichlet boundary condition, Neumann boundary condition, Marchenko equation, Lagrange interpolation series, sine-type function, Nevanlinna function.


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Article Information

TitleOn a generalization of the three spectral inverse problem
SourceMethods Funct. Anal. Topology, Vol. 22 (2016), no. 1, 74-80
MathSciNet   MR3522863
zbMATH 06630284
Milestones  Received 22/01/2015
CopyrightThe Author(s) 2016 (CC BY-SA)

Authors Information

O. P. Boyko
South Ukrainian National Pedagogical University, 26 Staroportofrankivs’ka, Odesa, 65020, Ukraine

O. M. Martynyuk
South Ukrainian National Pedagogical University, 26 Staroportofrankivs’ka, Odesa, 65020, Ukraine

V. N. Pivovarchik
South Ukrainian National Pedagogical University, 26 Staroportofrankivs’ka, Odesa, 65020, Ukraine


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Citation Example

O. P. Boyko, O. M. Martynyuk, and V. N. Pivovarchik, On a generalization of the three spectral inverse problem, Methods Funct. Anal. Topology 22 (2016), no. 1, 74-80.


BibTex

@article {MFAT842,
    AUTHOR = {Boyko, O. P. and Martynyuk, O. M. and Pivovarchik, V. N.},
     TITLE = {On a generalization of the three spectral inverse
problem},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {22},
      YEAR = {2016},
    NUMBER = {1},
     PAGES = {74-80},
      ISSN = {1029-3531},
  MRNUMBER = {MR3522863},
 ZBLNUMBER = {06630284},
       URL = {http://mfat.imath.kiev.ua/article/?id=842},
}


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