A SAMPLING THEOREM ASSOCIATED WITH A QUADRATIC PENCIL OF STURM-LIOUVILLE OPERATORS WITH PERIODIC COEFFICIENTS
ABDULLAH KABLAN *
Department of Mathematics, Faculty of Arts and Sciences, Gaziantep University, Gaziantep, 27310, Turkey
*Author to whom correspondence should be addressed.
Abstract
Kramer has developed a sampling theorem associated with n-th order self-adjoint differential operators. Recently this relation has been well developed. But the common property of the vast majority of papers is that the investigated boundary value problems have a simple eigenvalues. This paper is concerned with the application of the Kramer sampling theorem to a quadratic pencil of Sturm-Liouville operators with periodic coefficients. Such an operator may have multiple eigenvalues.
Keywords: Kramer's sampling theorem, eigenvalue problems, quadratic pencil of Sturm-Liouville operators