IJPAM: Volume 71, No. 2 (2011)
THE ZEROS OF ENTIRE FUNCTIONS OF SINE TYPE
Division of Physical and Computational Sciences
University of Pittsburgh at Bradford
Bradford, PA 16701, USA
Abstract. The main contribution of this paper is a result about the eigenvalues of two classes of Sturm-Liouville problems on a finite interval: if is the sequence of Dirichlet, respectively of Dirichlet-Robin eigenvalues of the canonical Sturm-Liouville operator with coefficient function (and boundary parameter - for the Dirichlet-Robin case), then , and respectively are the zeros of some entire functions of sine type .
Received: March 30, 2011
AMS Subject Classification: 42C99, 34A55, 34B24, 34L20
Key Words and Phrases: eigenvalues, eigenfunctions, characteristic functions of Sturm-Liouville operators, function of sine type, Riesz basis, Gelfand-Levitan kernel, Goursat problem
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395