Book Review: The kernel function and conformal mapping

Approximation of Conformal Mapping via the Szegő Kernel Method

We study the uniform approximation of the canonical conformal mapping, for a Jordan domain onto the unit disk, by polynomials generated from the partial sums of the Szegő kernel expansion. These polynomials converge to the conformal mapping uniformly on the closure of any Smirnov domain. We prove estimates for the rate of such convergence on domains with piecewise analytic boundaries, expressed...

Book Review: Music, Passion, and Cognitive Function

Book Review

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Conformal Mapping and Ellipses

We answer a question raised by M. Chuaqui, P. Duren, and B. Osgood by showing that a conformal mapping of a simply connected domain cannot take two circles onto two proper ellipses. The goal of this note is to prove the following. Proposition 1. Let Ω be a simply connected domain on C = C ∪ {∞} containing circles (on C) C1 and C2, C1 = C2. Let f be a conformal mapping from Ω into C. If f maps e...

Book Review: The CDA Book

they have additional information on their patients’ health and clinical statuses. The information could be acquired directly from patients or electronically from other providers through healthcare information exchanges (HIE). In the latter case, a common language or standard is necessary for sending and receiving digital forms of clinical data among healthcare organizations. On February 12, 200...