a2 Department of Mathematics, Saratov State University, Astrakhanskaya str. 83, 410012 Saratov, Russia (email: firstname.lastname@example.org)
a3 Fachbereich Mathematik, Universität Duisburg-Essen, D-47057 Duisburg, Germany (email: email@example.com)
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
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p1 Current address: Department of Mathematics and Physics, Qatar University, PO Box 2713 Doha, Qatar