Original scientific paper

Infinite product representation of solutions of indefinite problem with a finite number of arbitrary turning points

Hamidreza Marasi ; Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
Abdolbaghi Soltani
Aliasghar Jodayree Akbarfam

Abstract

In this paper we consider the Sturm-Liouville equation \(y''+(\rho^2\phi^2(x)-q(x))y=0\) on a finite interval I , say I=[0,1], under the assumption that I contains a finite number of arbitrary type turning points, which are zeros of \(\phi\) in I .
According to the four types of turning points, first we obtain the asymptotic forms of the solutions of (*) and then based on Hadamard's factorization theorem we use this asymptotic estimates to study the infinite product representation of solutions of such equations. Infinite product form of the solution has a basic application in studies of inverse spectral problems.

Keywords

Sturm-Liouville problem, turning point, asymptotic solution, Hadamard factorization theorem, infinite product representation, spectral theory

Hrčak ID:

303378

URI

https://hrcak.srce.hr/303378

Publication date:

2.6.2023.

Visits: 526 *