Czechoslovak Mathematical Journal, Vol. 49, No. 4, pp. 707-732, 1999

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

Milutin Dostanic

Matematicki fakultet, Studentski trg 16, 11000 Beograd, Yugoslavia, e-mail: domi@matf.bg.ac.yu

Abstract: We find an exact asymptotic formula for the singular values of the integral operator of the form $\int_{\Omega} T(x,y)k(x-y) \cdot\dd y L^2 (\Omega)\rightarrow L^2(\Omega)$ ($\Omega\subset\Bbb R^m$, a Jordan measurable set) where $k(t) = k_0((t^2_1 + t^2_2 + \ldots t^2_m)^{\frac{m}2})$, $k_0 (x) = x^{\alpha-1} L(\tfrac1x)$, $\tfrac12 - \tfrac1{2m}< \alpha< \tfrac12$ and $L$ is slowly varying function with some additional properties. The formula is an explicit expression in terms of $L$ and $T$.

Classification (MSC 1991): 47B10


Full text available as PDF (smallest), as compressed PostScript (.ps.gz) or as raw PostScript (.ps).

Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.
Subscribers of Springer (formerly Kluwer) need to access the articles on their site, which is http://www.springeronline.com/10587.


[Previous Article] [Next Article] [Contents of This Number] [Contents of Czechoslovak Mathematical Journal]