Title

On The Inversion Of Integral Transforms Associated With Sturm-Liouville Problems

Abstract

Consider the Sturm-Liouville boundary-value problem 1. (1) y″ - q(x) y = -t2y, -∞ < a ≤ x ≤ b < ∞ 2. (2) y(a) cos α + y′(a) sin α = 0 3. (3) y(b) cos β + y′(b) sin β = 0, where q(x) is continuous on [a, b]. Let φ(x, t) be a solution of either the initial-value problem (1) and (2) or (1) and (3). In this paper we develop two techniques to invert the integral F(t) = ∝abf(x) φ(x, t) dx, where f(x) ε{lunate} L2(a, b); one technique is based on the construction of some biorthogonal sequence of functions and the other is based on Poisson's summation formula. © 1992.

Publication Date

1-1-1992

Publication Title

Journal of Mathematical Analysis and Applications

Volume

164

Issue

1

Number of Pages

285-306

Document Type

Article

Identifier

scopus

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/0022-247X(92)90157-9

Socpus ID

38249013624 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/38249013624

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