TY  - JOUR
ID  - Castro2012
LB  - Castro2012
AU  - Castro, Luis P.
AU  - Saitoh, Saburou
AU  - Tuan, Nguyen Minh
TI  - Convolutions, integral transforms and integral equations by means of the theory of reproducing kernels
ST  - Convolutions, integral transforms and integral equations by means of the theory of reproducing kernels
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2012
VL  - 32
IS  - 4
SP  - 633
EP  - 646
DO  - http://dx.doi.org/10.7494/OpMath.2012.32.4.633
UR  - http://dx.doi.org/10.7494/OpMath.2012.32.4.633
AB  - 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).
KW  - Hilbert space
KW  - linear transform
KW  - reproducing kernel
KW  - linear mapping
KW  - convolution
KW  - norminequality
KW  - integral equation
KW  - Tikhonov regularization
SN  - 1232-9274
ER  -