Abstract

We find the exact asymptotic behaviour of singular values of the operator $CP_h$, where $C$ is the integral Cauchy's operator and $P_h$ integral operator with the kernel $$K\left( z,\zeta\right) =\frac{\left( 1-\vert z\vert^2\vert\zeta\vert^2\right)^2} {\pi\vert 1-z\overline{\zeta }\vert^4}-\frac{2}{\pi }\ \frac{\vert z\vert^2\vert\zeta\vert^2} {\vert 1-z\overline{\zeta }\vert^2}.$$

Keywords: Bergman space; Cauchy operator; asymptotics of eigenvalues.

MSC: 47G10, 45P05

Pages:  63--67     

Volume  62 ,  Issue  1 ,  2010