| Title:
|
Integro-differential-difference equations associated with the Dunkl operator and entire functions (English) |
| Author:
|
Salem, Néjib Ben |
| Author:
|
Kallel, Samir |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
4 |
| Year:
|
2004 |
| Pages:
|
699-725 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this work we consider the Dunkl operator on the complex plane, defined by $$ \Cal D_k f(z)=\frac{d}{dz}f(z)+k\frac{f(z)-f(-z)}{z}, k\geq 0. $$ We define a convolution product associated with $\Cal D_k$ denoted $\ast_k$ and we study the integro-differential-difference equations of the type $\mu \ast_k f=\sum_{n=0}^{\infty}a_{n,k}\Cal D^n_k f$, where $(a_{n,k})$ is a sequence of complex numbers and $\mu $ is a measure over the real line. We show that many of these equations provide representations for particular classes of entire functions of exponential type. (English) |
| Keyword:
|
Dunkl operator |
| Keyword:
|
Fourier-Dunkl transform |
| Keyword:
|
entire function of exponential type |
| Keyword:
|
integro-differential-difference equation |
| MSC:
|
30D05 |
| MSC:
|
30D15 |
| MSC:
|
33E30 |
| MSC:
|
34K99 |
| MSC:
|
34M05 |
| MSC:
|
44A35 |
| MSC:
|
45J05 |
| idZBL:
|
Zbl 1098.30019 |
| idMR:
|
MR2103085 |
| . |
| Date available:
|
2009-05-05T16:48:31Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119495 |
| . |
| 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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| . |
