International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 9, Pages 479-485
doi:10.1155/S0161171204208274
Interpolation methods to estimate eigenvalue distribution of some integral operators
1Department of Mathematics, Faculty of Science, Ain Shams University, Cairo 11566, Egypt
2Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11566, Egypt
Received 20 August 2002
Copyright © 2004 E. M. El-Shobaky et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We study the asymptotic distribution of eigenvalues of
integral operators Tk defined by kernels k which
belong to Triebel-Lizorkin function space Fpuσ(F qvτ) by using the factorization theorem and
the Weyl numbers xn. We use the relation between
Triebel-Lizorkin space Fpuσ(Ω) and Besov
space Bpqτ(Ω) and the interpolation
methods to get an estimation for the distribution
of eigenvalues in Lizorkin spaces Fpuσ(F qvτ).