| Title:
|
A Parseval equation and a generalized finite Hankel transformation (English) |
| Author:
|
Betancor, Jorge J. |
| Author:
|
Flores, Manuel T. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
627-638 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $$ \langle (h'_\mu f), ((h_\mu ^{\ast } \varphi )(n))_{n=0}^{\infty }\rangle =\langle f,\varphi \rangle, \quad \text{for } \varphi \in S_\mu . $$ (English) |
| Keyword:
|
finite Hankel transformation |
| Keyword:
|
distribution |
| Keyword:
|
Parseval equation |
| MSC:
|
44A15 |
| MSC:
|
46F12 |
| idZBL:
|
Zbl 0763.46028 |
| idMR:
|
MR1159809 |
| . |
| Date available:
|
2009-01-08T17:47:42Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118442 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
