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On Barcilon’s formula for Krein’s string


We find conditions on two sequences of positive numbers that are sufficient for the sequences to be the Neumann and the Dirichlet spectra of a Krein string such that Barcilon’s formula holds true.

Key words: Coefficient of dynamic compliance, density, eigenvalues, spectral function, S-function, regular string.

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Article Information

TitleOn Barcilon’s formula for Krein’s string
SourceMethods Funct. Anal. Topology, Vol. 23 (2017), no. 3, 270-276
MathSciNet   MR3707521
Milestones  Received 21.11.2016; Revised 07/05/2017
CopyrightThe Author(s) 2017 (CC BY-SA)

Authors Information

I. S. Kac
Odessa National Academy of Food Technologies, 112 Kanatnaya, Odessa, 65039, Ukraine

V. Pivovarchik
South Ukrainian National Pedagogical University, 26 Staroportofrankovskaya, Odessa, 65020, Ukraine 

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Citation Example

I. S. Kac and V. N. Pivovarchik, On Barcilon’s formula for Krein’s string, Methods Funct. Anal. Topology 23 (2017), no. 3, 270-276.


@article {MFAT988,
    AUTHOR = {Kac, I. S. and Pivovarchik, V. N.},
     TITLE = {On Barcilon’s formula for Krein’s string},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {23},
      YEAR = {2017},
    NUMBER = {3},
     PAGES = {270-276},
      ISSN = {1029-3531},
  MRNUMBER = {MR3707521},
       URL = {},


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