Fractional Cauchy transforms
著者
書誌事項
Fractional Cauchy transforms
（Chapman & Hall/CRC monographs and surveys in pure and applied mathematics, ; 136）
Chapman & Hall/CRC, 2006
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
Presenting new results along with research spanning five decades, Fractional Cauchy Transforms provides a full treatment of the topic, from its roots in classical complex analysis to its current state. Self-contained, it includes introductory material and classical results, such as those associated with complex-valued measures on the unit circle, that form the basis of the developments that follow. The authors focus on concrete analytic questions, with functional analysis providing the general framework.
After examining basic properties, the authors study integral means and relationships between the fractional Cauchy transforms and the Hardy and Dirichlet spaces. They then study radial and nontangential limits, followed by chapters devoted to multipliers, composition operators, and univalent functions. The final chapter gives an analytic characterization of the family of Cauchy transforms when considered as functions defined in the complement of the unit circle.
About the authors:
Rita A. Hibschweiler is a Professor in the Department of Mathematics and Statistics at the University of New Hampshire, Durham, USA.
Thomas H. MacGregor is Professor Emeritus, State University of New York at Albany and a Research Associate at Bowdoin College, Brunswick, Maine, USA.\
目次
Introduction. Basic Properties of fa o. Integral Means and the Hardy and Dirichlet Spaces. Radial Limits. Zeros. Multipliers: Basic Results. Multipliers: Further Results. Composition. Univalent Functions. A Characterization of Cauchy Transforms.
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