Geodesic
A Parseval equation and a generalized finite Hankel transformation
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 4, pp. 627-638.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In this paper, we study the finite Hankel transformation on spaces of ge\-ne\-ra\-lized functions by developing a new procedure. We consider two Hankel type integral transformations $h_\mu $ and $h_\mu ^{\ast }$ connected by the Parseval equation $$ \sum_{n=0}^{\infty }(h_\mu f)(n)(h_\mu ^{\ast } \varphi )(n)= \int_{0}^{1}f(x)\varphi (x)\, dx. $$ A space $S_\mu $ of functions and a space $L_\mu $ of complex sequences are introduced. $h_\mu ^{\ast }$ is an isomorphism from $S_\mu $ onto $L_\mu $ when $\mu \geq -\frac{1}{2}$. We propose to define the generalized finite Hankel transform $h'_\mu f$ of $f\in S'_\mu $ by $$ \langle (h'_\mu f), ((h_\mu ^{\ast } \varphi )(n))_{n=0}^{\infty }\rangle =\langle f,\varphi \rangle, \quad \text{for } \varphi \in S_\mu . $$
Classification : 44A15, 46F12
Keywords: finite Hankel transformation; distribution; Parseval equation 
@article{CMUC_1991__32_4_a4,
     author = {Betancor, Jorge J. and Flores, Manuel T.},
     title = {A {Parseval} equation and a generalized finite {Hankel} transformation},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {627--638},
     publisher = {mathdoc},
     volume = {32},
     number = {4},
     year = {1991},
     mrnumber = {1159809},
     zbl = {0763.46028},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1991__32_4_a4/}
}
TY  - JOUR
AU  - Betancor, Jorge J.
AU  - Flores, Manuel T.
TI  - A Parseval equation and a generalized finite Hankel transformation
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1991
SP  - 627
EP  - 638
VL  - 32
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_1991__32_4_a4/
LA  - en
ID  - CMUC_1991__32_4_a4
ER  - 
%0 Journal Article
%A Betancor, Jorge J.
%A Flores, Manuel T.
%T A Parseval equation and a generalized finite Hankel transformation
%J Commentationes Mathematicae Universitatis Carolinae
%D 1991
%P 627-638
%V 32
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_1991__32_4_a4/
%G en
%F CMUC_1991__32_4_a4
Betancor, Jorge J.; Flores, Manuel T. A Parseval equation and a generalized finite Hankel transformation. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 4, pp. 627-638. http://geodesic.mathdoc.fr/item/CMUC_1991__32_4_a4/