Open AccessThe eigenvalues’ function of the family of Sturm-Liouville operators and the inverse problems
Author(s) -
Tigran Harutyunyan
Publication year - 2019
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.50.2019.3352
Subject(s) - sturm–liouville theory , mathematics , eigenvalues and eigenvectors , inverse , function (biology) , pure mathematics , boundary (topology) , operator (biology) , mathematical analysis , boundary value problem , chemistry , biochemistry , repressor , gene , transcription factor , physics , geometry , quantum mechanics , evolutionary biology , biology
We study the direct and inverse problems for the family of Sturm-Liouville operators, generated by fixed potential q and the family of separated boundary conditions. We prove that the union of the spectra of all these operators can be represented as a smooth surface (as the values of a real analytic function of two variables), which has specific properties. We call this function ”the eigenvalues function of the family of Sturm-Liouville operators (EVF)”. From the properties of this function we select those, which are sufficient for a function of two variables be the EVF a family of Sturm-Liouville operators.