Open Access

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.

Full Text

Article Information

TitleOn Barcilon’s formula for Krein’s string
SourceMethods Funct. Anal. Topology, Vol. 23 (2017), no. 3, 270-276
MilestonesReceived 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 

Google Scholar Metrics

Citing articles in Google Scholar
Similar articles in Google Scholar

Export article

Save to Mendeley

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},
       URL = {},


Coming Soon.

All Issues