The eigenvalues’ function of the family of Sturm-Liouville operators and the inverse problems | Zendy

Tigran Harutyunyan | Zendy

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The 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.

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