Opuscula Math. 32, no. 4 (2012), 633-646
http://dx.doi.org/10.7494/OpMath.2012.32.4.633

 
Opuscula Mathematica

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

Luis P. Castro
Saburou Saitoh
Nguyen Minh Tuan

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.

Mathematics Subject Classification: 30C40, 42A85, 45E10, 44A20, 46H05.

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Cite this article as:
Luis P. Castro, Saburou Saitoh, Nguyen Minh Tuan, Convolutions, integral transforms and integral equations by means of the theory of reproducing kernels, Opuscula Math. 32, no. 4 (2012), 633-646, http://dx.doi.org/10.7494/OpMath.2012.32.4.633

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