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Mathematical Notes

, Volume 77, Issue 5–6, pp 777–786 | Cite as

The Norm and Regularized Trace of the Cauchy Transform

  • M. R. Dostanic
Article

Abstract

In this paper, the norm of the Cauchy transform C is obtained on the space L2(D, dμ), where dμ = ω(|z|) dA(z). Also, (for the case ω ≡ 1), the first regularized trace of the operator C* C on L2(Ω) is obtained. The results are illustrated by examples, with different specific choices of the function ω and the domain Ω.

Key words

Cauchy transform regularized trace operator function space boundary-value problem Bessel function Parseval’s equality 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • M. R. Dostanic
    • 1
  1. 1.Mathematics Dept.Belgrade UniversitySerbia and MontenegroYugoslavia

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