Exact asymptotic behavior of singular values of a class of integral operators

Title:

Exact asymptotic behavior of singular values of a class of integral operators

Creator:

Dostanić, Milutin

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a744933d-881c-4575-bafe-b47321a44877
uuid:a744933d-881c-4575-bafe-b47321a44877

Subject:

math, exact asymptotic formula, and integral operators

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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 $T$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

707-732

Source:

Czechoslovak Mathematical Journal | 1999 Volume:49 | Number:4

Harvested from:

CDK

Metadata only:

false