Opuscula Math. 32, no. 4 (2012), 633-646
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.
About the authors ▼
Luis P. Castro
Department of Mathematics and CIDMA-Center for Research and Development in Mathematics and Applications,University of Aveiro, 3810-193 Aveiro, Portugal
Saburou Saitoh
Department of Mathematics and CIDMA-Center for Research and Development in Mathematics and Applications, University of Aveiro, 3810-193 Aveiro, Portugal
Nguyen Minh Tuan
Hanoi National University, University of Education, Department of Mathematics, G7 build., 144 Xuan Thuy str. Cau Giay dist., Hanoi, Vietnam
About the article ▼
Received: 2011-05-07.
Accepted: 2011-12-20.
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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