The Norm and Regularized Trace of the Cauchy Transform
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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 wordsCauchy transform regularized trace operator function space boundary-value problem Bessel function Parseval’s equality
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