Open AccessON THE EXPANSION FORMULA FOR A SINGULAR STURM-LIOUVILLE OPERATOR
Author(s) -
Ulviye Demirbilek,
Khanlar R. Mamedov
Publication year - 2021
Publication title -
journal of science and arts
Language(s) - English
Resource type - Journals
eISSN - 2068-3049
pISSN - 1844-9581
DOI - 10.46939/j.sci.arts-21.1-a07
Subject(s) - eigenfunction , sturm–liouville theory , mathematics , resolvent , mathematical analysis , operator (biology) , boundary value problem , kernel (algebra) , spectral theory of ordinary differential equations , asymptotic expansion , eigenvalues and eigenvectors , pure mathematics , physics , quasinormal operator , finite rank operator , chemistry , quantum mechanics , biochemistry , repressor , transcription factor , banach space , gene
In this study, on the semi-axis, Sturm - Liouville problem under boundary condition depending on spectral parameter is considered. In what follows scattering data is defined and its properties are given for the problem. The kernel of resolvent operator which is Green function is constructed. Using Titchmarsh method, expansion is obtained according to eigenfunctions and expansion formula is expressed with the scattering data.