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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


Puni tekst: engleski pdf 226 Kb

str. 49-67

preuzimanja: 157

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Sažetak

In this paper we consider the Sturm-Liouville equation y+(ρ2ϕ2(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 ϕ 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.

Ključne riječi

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

Hrčak ID:

303378

URI

https://hrcak.srce.hr/303378

Datum izdavanja:

2.6.2023.

Posjeta: 635 *

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