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Three spectra problems for star graph of Stieltjes strings


Abstract

The (main) spectral problem for a star graph with three edges composed of Stieltjes strings is considered with the Dirichlet conditions at the pendant vertices. In addition we consider the Dirichlet-Neumann problem on the first edge (Problem 2) and the Dirichlet-Dirichlet problem on the union of the second and the third strings (Problem 3). It is shown that the spectrum of the main problem interlace (in a non-strict sense) with the union of spectra of Problems 2 and 3. The inverse problem lies in recovering the masses of the beads (point masses) and the lengths of the intervals between them using the spectra of the main problem and of Problems 2 and 3. Conditions on three sequences of numbers are proposed sufficient to be the spectra of the main problem and of Problems 2 and 3, respectively.

Key words: Eigenvalue, Lagrange interpolating polynomial, continued fraction, Dirichlet boundary condition.


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Article Information

TitleThree spectra problems for star graph of Stieltjes strings
SourceMethods Funct. Anal. Topology, Vol. 25 (2019), no. 4, 311-323
MilestonesReceived 28/06/2019
CopyrightThe Author(s) 2019 (CC BY-SA)

Authors Information

A. Dudko
South-Ukrainian National Pedagogical University, named after K. D. Ushynsky, Staroportofrankovskaya str. 26, Odesa, Ukraine, 65020

V. Pivovarchik
South-Ukrainian National Pedagogical University, named after K. D. Ushynsky, Staroportofrankovskaya str. 26, Odesa, Ukraine, 65020


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Citation Example

A. Dudko and V. Pivovarchik, Three spectra problems for star graph of Stieltjes strings, Methods Funct. Anal. Topology 25 (2019), no. 4, 311-323.


BibTex

@article {MFAT1240,
    AUTHOR = {A. Dudko and V. Pivovarchik},
     TITLE = {Three spectra problems for star graph of Stieltjes strings},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {25},
      YEAR = {2019},
    NUMBER = {4},
     PAGES = {311-323},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=1240},
}


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