Exact asymptotic behavior of singular values of a class of integral operators
Czechoslovak Mathematical Journal, Tome 49 (1999) no. 4, pp. 707-732
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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 $T$.
@article{CMJ_1999__49_4_a4,
author = {Dostani\'c, Milutin},
title = {Exact asymptotic behavior of singular values of a class of integral operators},
journal = {Czechoslovak Mathematical Journal},
pages = {707--732},
publisher = {mathdoc},
volume = {49},
number = {4},
year = {1999},
mrnumber = {1746699},
zbl = {1008.47045},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMJ_1999__49_4_a4/}
}
TY - JOUR AU - Dostanić, Milutin TI - Exact asymptotic behavior of singular values of a class of integral operators JO - Czechoslovak Mathematical Journal PY - 1999 SP - 707 EP - 732 VL - 49 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/CMJ_1999__49_4_a4/ LA - en ID - CMJ_1999__49_4_a4 ER -
Dostanić, Milutin. Exact asymptotic behavior of singular values of a class of integral operators. Czechoslovak Mathematical Journal, Tome 49 (1999) no. 4, pp. 707-732. http://geodesic.mathdoc.fr/item/CMJ_1999__49_4_a4/