| Title:
|
Exact asymptotic behavior of singular values of a class of integral operators (English) |
| Author:
|
Dostanić, Milutin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
49 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
707-732 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We find an exact asymptotic formula for the singular values of the integral operator of the form $\int _{\Omega } T(x,y)k(x-y) \cdot \mathrm{d}y \: L^2 (\Omega )\rightarrow L^2(\Omega )$ ($\Omega \subset \mathbb{R}^m$, a Jordan measurable set) where $k(t) = k_0((t^2_1 + t^2_2 + \ldots t^2_m)^{\frac{m}{2}})$, $k_0 (x) = x^{\alpha -1} L(\tfrac{1}{x})$, $\tfrac{1}{2} - \tfrac{1}{2m}< \alpha < \tfrac{1}{2}$ and $L$ is slowly varying function with some additional properties. The formula is an explicit expression in terms of $L$ and $T$. (English) |
| MSC:
|
47B10 |
| MSC:
|
47G10 |
| idZBL:
|
Zbl 1008.47045 |
| idMR:
|
MR1746699 |
| . |
| Date available:
|
2009-09-24T10:26:57Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127523 |
| . |
| Reference:
|
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| Reference:
|
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| . |
