The theory of reproducing kernels started with two papers of 1921 [449] and 1922 [45] which
dealt with typical reproducing kernels of Szegö and Bergman, and since then the theory has …

This paper shows that there is a fruitful world behind sampling theorems. For this purpose,
the sampling problem is reformulated from a functional analytic standpoint, and is …

Let H be a Hilbert space, W a closed subspace of H, and Q a (linear bounded) projection
from H onto W with null space M⊥. We study decompositions like Qf=∑ n∊ ℕ< f, hn> fn …

The purpose of this paper is to deal with the problem of recovering a signal from its noisy
version. One example is to restore old images degraded by noise. The recovery solution is …

Wavelets, known to be useful in nonlinear multiscale processes and in multiresolution
analysis, are shown to have aq-deformed algebraic structure. The translation and dilation …

In Chap. 2, which is at the heart of this book, we develop the general theory of reproducing
kernels and its fundamental properties. First, we establish that any positive definite kernel …

Application of the Daubechies compact support wavelets to problems of nonrelativistic
potential scattering described by integral Lippmann-Schwinger equation is discussed …

As stated in the preface, one of our strong motivations for writing this book is given by the
historical success of the numerical and real inversion formulas of the Laplace transform …

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