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.
- 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
- Received: 2011-05-07.
- Accepted: 2011-12-20.
