Open Access

On a generalization of the three spectral inverse problem

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.

Article Information

 Title On a generalization of the three spectral inverse problem Source Methods Funct. Anal. Topology, Vol. 22 (2016), no. 1, 74-80 MathSciNet MR3522863 zbMATH 06630284 Milestones Received 22/01/2015 Copyright The 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

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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