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Published in:
The Reproducing Kernel Property and Its Space: The Basics Read chapter Read first chapter

2015 | OriginalPaper | Chapter

5. Sampling Theory and Reproducing Kernel Hilbert Spaces

Author : Antonio G. García

Published in: Operator Theory

Publisher: Springer Basel

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Abstract

This work intends to serve as an introduction to sampling theory. Basically, sampling theory deals with the reconstruction of functions through their values on an appropriate sequence of points by means of sampling expansions involving these values. Reproducing kernel Hilbert spaces are suitable spaces for sampling purposes since evaluation functionals are continuous. As a consequence, the recovery of any function from a sequence of its samples depends on the basis properties of the reproducing kernel at the sampling points.

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previous chapter Bergman Kernel in Complex Analysis
next chapter Reproducing Kernels in Coherent States, Wavelets, and Quantization
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Metadata
Title
Sampling Theory and Reproducing Kernel Hilbert Spaces
Author
Antonio G. García
Copyright Year
2015
Publisher
Springer Basel
Book
Operator Theory

Print ISBN: 978-3-0348-0666-4

Electronic ISBN: 978-3-0348-0667-1

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-0348-0667-1_64

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