Generalized Hermite Interpolation and Sampling Theorem Involving Derivatives
Commun. Korean Math. Soc. 2002 Vol. 17, No. 4, 731-740
Printed December 1, 2002
Chang Eon Shin
Sogang University
Abstract : We derive the generalized Hermite interpolation by using the contour integral and extend the generalized Hermite interpolation to obtain the sampling expansion involving derivatives for band-limited functions $f$, that is, $f$ is an entire function satisfying the following growth condition $$ |f(z)|\le A \, \exp(\sigma |y|) \,\, \text{for some }A, \, \sigma>0 \, \, \text{and any } z=x+iy \in \Bbb C. $$
Keywords : generalized Hermite interpolation, sampling theorem, contour integral
MSC numbers : 94A12
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