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J. Korean Math. Soc. 2016; 53(5): 969-990

Printed September 1, 2016

https://doi.org/10.4134/JKMS.j150226

Copyright © The Korean Mathematical Society.

Sampling theorems associated with differential operators with finite rank perturbations

Mahmoud H. Annaby, Omar H. El-Haddad, and Hassan A. Hassan

Cairo University, Cairo University, Faculty of Basic Education

Abstract

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We derive a sampling theorem associated with first order self-adjoint eigenvalue problem with a finite rank perturbation. The class of the sampled integral transforms is of finite Fourier type where the kernel has an additional perturbation.

Keywords: Green's function, eigenfunctions expansions, finite rank pertur\-bations

MSC numbers: 34B27, 34L10, 81Q15

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