Abstract
In this paper, the norm of the Cauchy transform C is obtained on the space L 2(D, dμ), where dμ = ω(|z|) dA(z). Also, (for the case ω ≡ 1), the first regularized trace of the operator C* C on L 2(Ω) is obtained. The results are illustrated by examples, with different specific choices of the function ω and the domain Ω.
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Translated from Matematicheskie Zametki, vol. 77, no. 6, 2005, pp. 844–853.
Original Russian Text Copyright ©2005 by M. R. Dostanic.
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Dostanic, M.R. The Norm and Regularized Trace of the Cauchy Transform. Math Notes 77, 777–786 (2005). https://doi.org/10.1007/s11006-005-0078-z
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DOI: https://doi.org/10.1007/s11006-005-0078-z