Sampling Theory and Reproducing Kernel Hilbert Spaces

Antonio G. García ()
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Antonio G. García: Departamento de Matemáticas, Universidad Carlos III de Madrid

Chapter 5 in Operator Theory, 2015, pp 87-110 from Springer

Abstract: 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.

Keywords: Reproducing Kernel; Paley-Wiener Space; Shift-invariant Spaces; Riesz Basis; Sampling Formula (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0667-1_64

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DOI: 10.1007/978-3-0348-0667-1_64

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