MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Cauchy operator on Bergman space of harmonic functions on unit disk
Milutin R. Dostanić

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 $$ K\left( z,\zeta\right) =\frac{\left( 1-\vert z\vert^2\vert\zeta\vert^2\right)^2} {\pi\vert 1-z\overline{\zeta }\vert^4}-\frac{2}{\pi }\ \frac{\vert z\vert^2\vert\zeta\vert^2} {\vert 1-z\overline{\zeta }\vert^2}. $$

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

MSC: 47G10, 45P05

Pages:  63--67     

Volume  62 ,  Issue  1 ,  2010