Convolutions, integral transforms and integral equations by means of the theory of reproducing kernels

Abstract

This paper introduces a general concept of convolutions by means of the theory of reproducing kernels which turns out to be useful for several concrete examples and applications. Consequent properties are exposed (including, in particular, associated norm inequalities).

Keywords

• Hilbert space
• linear transform
• reproducing kernel
• linear mapping
• convolution
• norminequality
• integral equation
• Tikhonov regularization