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SAMPLING AND BIRKHOFF REGULAR PROBLEMS

Part of:Communication, informationBoundary value problems

Published online by Cambridge University Press:  15 December 2009

M. H. ANNABY,
S. A. BUTERIN and
G. FREILING
M. H. ANNABY*
Affiliation:
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt (email: mannaby@qu.edu.qa, mhannaby@yahoo.com)
S. A. BUTERIN
Affiliation:
Department of Mathematics, Saratov State University, Astrakhanskaya str. 83, 410012 Saratov, Russia (email: buterinsa@info.sgu.ru)
G. FREILING
Affiliation:
Fachbereich Mathematik, Universität Duisburg-Essen, D-47057 Duisburg, Germany (email: freiling@math.uni-duisburg.de)
*
✉For correspondence; e-mail: mannaby@qu.edu.qa,mhannaby@yahoo.com
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Abstract

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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.

Keywords

sampling theoryLagrange and Hermite interpolationBirkhoff regular eigenvalue problems

MSC classification

Secondary:34B05: Linear boundary value problems94A20: Sampling theory

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 87 , Issue 3 , December 2009, pp. 289 - 310
Copyright
Copyright © Australian Mathematical Publishing Association, Inc. 2009

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