| Title:
|
On the Fourier cosine—Kontorovich-Lebedev generalized convolution transforms (English) |
| Author:
|
Hong, Nguyen Thanh |
| Author:
|
Tuan, Trinh |
| Author:
|
Thao, Nguyen Xuan |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
58 |
| Issue:
|
4 |
| Year:
|
2013 |
| Pages:
|
473-486 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We deal with several classes of integral transformations of the form $$ \label {generalformula} f(x)\rightarrow D\int _{\mathbb R_+^2} \frac 1u ({\rm e}^{-u\cosh (x+v)}+{\rm e}^{-u\cosh (x-v)}) h(u)f(v) {\rm d}u {\rm d} v, $$ where $D$ is an operator. In case $D$ is the identity operator, we obtain several operator properties on $L_p(\mathbb R_+)$ with weights for a generalized operator related to the Fourier cosine and the Kontorovich-Lebedev integral transforms. For a class of differential operators of infinite order, we prove the unitary property of these transforms on $L_2(\mathbb R_+)$ and define the inversion formula. Further, for an other class of differential operators of finite order, we apply these transformations to solve a class of integro-differential problems of generalized convolution type. (English) |
| Keyword:
|
convolution |
| Keyword:
|
Hölder inequality |
| Keyword:
|
Young's theorem |
| Keyword:
|
Watson's theorem |
| Keyword:
|
unitary |
| Keyword:
|
Fourier cosine |
| Keyword:
|
Kontorovich-Lebedev |
| Keyword:
|
transform |
| Keyword:
|
integro-differential equation |
| MSC:
|
33C10 |
| MSC:
|
44A35 |
| MSC:
|
45E10 |
| MSC:
|
45J05 |
| MSC:
|
47A30 |
| MSC:
|
47B15 |
| idZBL:
|
Zbl 06221241 |
| idMR:
|
MR3083524 |
| DOI:
|
10.1007/s10492-013-0023-5 |
| . |
| Date available:
|
2013-07-18T15:20:53Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143341 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| . |
