On Green's function of two-parameter problems and sampling theory

Abstract

In this article, we introduce two-dimensional sampling theorems associated with first and second order two-parameter differential equations. We define two-dimensional integral transforms in terms of Green's function of the problem and derive associated sampling theorems. The sampling series in the first order two-parameter case is a generalization of a two-dimensional version of the Whittaker–Kotel'nikov–Shannon sampling theorem. The second order two-parameter systems of differential equations are also considered and associated sampling expansions are derived.

Keywords:

• multiparameter eigenvalue problems
• Green's function
• sampling theory

AMS Subject Classifications::

• 32A15
• 34B08
• 94A20