Spectral asymptotic of Cauchy’s operator on harmonic Bergman space for a simply connected domain

Abstract

We find the asymptotic behaviour of the singular numbers for the Cauchy operator restricted to the harmonic subspace i.e. Here is the orthogonal projection from onto Moreover, we give lower and upper asymptotic estimate bounds for

where is a conformal mapping.

Keywords:

• Cauchy operator
• harmonic functions
• simply connected domain
• singular numbers

AMS Subject Classifications:

• Primary: 31A10
• 30H20

Notes

No potential conflict of interest was reported by the author.