Functional Analysis and Applications Seminar 

12/05/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building
Anthippi Poulkou, University of Athens Panepistimioupolis, Grécia

Sampling and interpolation theories associated with boundary value problems

This talk deals with joint work with W.N. Everritt. The link of the sampling/interpolation theorem of Shannon-Whittaker with the original Kramer sampling theorem is considered. Also, the connection of these two significant results with boundary value problems associated with linear ordinary differential equations as defined on intervals of real line is specified. The results given in this talk are concerned with the generation from first-order linear, ordinary boundary value problems of Kramer analytic kernels which introduce analytic dependence of the kernel on the sampling parameter. These kernels are represented by unbounded self-adjoint differential operators in Hilbert function spaces. Necessary and sufficient conditions are given to ensure that these differential operators have a simple, discrete spectrum which then allows the introduction of the associated Kramer analytic kernels. Finally, the corresponding analytic interpolation functions are defined with the required properties, to give the Lagrange interpolation series.