The equiconvergence of the eigenfunction expansion for a singular version of one-dimensional Schrodinger operator with explosive factor

Abstract

This paper is devoted to prove the equiconvergence formula of the eigenfunction expansion for some version of Schrodinger operator with explosive factor. The analysis relies on asymptotic calculation and complex integration. The paper is of great interest for the community working in the area.

The inverse spectral problem of some singular version of one-dimensional Schrödinger operator with explosive factor in finite interval

“…From (2.57) and the representation (2.53) and By using the same proof technique of Theorem 2.1 we get the integral equation 3-The present problem, with yð0Þ ¼ 0; yðpÞ ¼ 0 cannot considered as a spacial case of (4.61) 4-Due to the absence of the numbers Hand h the inverse problem by two specters cannot be studied in the present work 5-Besides the direct spectral investigation of the of the present problem as in [14,16], the author had studied the eigenfunction expansion, equiconvergence of the eigenfunction expansion, and the regularized trace formula, [20,21] …”