Journal of the Australian Mathematical Society

Table of Contents - 2009 - Volume 87, Issue 03  

Research Article

SAMPLING AND BIRKHOFF REGULAR PROBLEMS

M. H. ANNABYa1 p1 c1, S. A. BUTERINa2 and G. FREILINGa3

a1 Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt (email: mannaby@qu.edu.qa, mhannaby@yahoo.com)

a2 Department of Mathematics, Saratov State University, Astrakhanskaya str. 83, 410012 Saratov, Russia (email: buterinsa@info.sgu.ru)

a3 Fachbereich Mathematik, Universität Duisburg-Essen, D-47057 Duisburg, Germany (email: freiling@math.uni-duisburg.de)

Abstract

We establish new sampling representations for linear integral transforms associated with arbitrary general Birkhoff regular boundary value problems. The new approach is developed in connection with the analytical properties of Green’s function, and does not require the root functions to be a basis or complete. Unlike most of the known sampling expansions associated with eigenvalue problems, the results obtained are, generally speaking, of Hermite interpolation type.

(Received February 06 2008)

(Accepted July 03 2009)

2000 Mathematics subject classification

  • primary 34B05; secondary 30D10;
  • 94A20

Keywords and phrases

  • sampling theory;
  • Lagrange and Hermite interpolation;
  • Birkhoff regular eigenvalue problems

Correspondence:

c1 For correspondence; e-mail: mannaby@qu.edu.qa,mhannaby@yahoo.com

p1 Current address: Department of Mathematics and Physics, Qatar University, PO Box 2713 Doha, Qatar