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.
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.
BibTex
@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 = {http://mfat.imath.kiev.ua/article/?id=988},
}