Fractional Cauchy transforms /
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...
| Main Authors: | , |
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| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Boca Raton :
Chapman and Hall/CRC,
2019.
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| Edition: | 1st. |
| Series: | Monographs and Surveys in Pure and Applied Mathematics
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | 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. |
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| Item Description: | Previously issued in print: 2005. INTRODUCTION Definition of the families Fa Relations between F1and H1 The Riesz-Herglotz formula Representations with real measures and h1 The F. and M. Riesz theorem The representing measures for functions in F1 The one-to-one correspondence between measures and functions in the Riesz-Herglotz formula The Banach space structure of Fa Norm convergence and convergence uniform on compact sets Notes BASIC PROPERTIES OF Fa o Properties of the gamma function and the binomial coefficients A product theorem Membership of f and f ' in Fa The inclusion of Fa in Fb when 0 = a |
| Physical Description: | 1 online resource. |
| ISBN: | 9780429525063 0429525060 9780429144226 0429144229 9781420034875 1420034871 |