A01=Rita A. Hibschweiler
A01=Thomas H. MacGregor
advanced complex analysis techniques
Alaoglu
analytic functions
Author_Rita A. Hibschweiler
Author_Thomas H. MacGregor
Banach
Banach Alaoglu Theorem
Banach Space
Besov Space
Blaschke
Blaschke Product
Category=PBKF
Cauchy Transforms
classical complex analysis
Closed Convex Hull
Compact
complex measures
Composition Operator
composition operators
Conformal Automorphism
Constant
Continuous Linear Operator
Dirichlet Space
Dirichlet spaces
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Finite Blaschke Product
fractional Cauchy transforms
Fractional Derivatives
functional analysis
Hadamard Product
Hardy Spaces
Harmonic Classes
integral means
Jensen's Formula
Jensen’s Formula
Logarithmic Capacity
Montel's Theorem
Montel’s Theorem
Nevanlinna Class
Nonnegative Integer
Nontangential Limit
Positive
Positive Constant
Product
radial boundary behavior
Radial Limit
Space
Subharmonic Functions
Subsets
Theorem
Total Variation Norm
univalent mappings
Product details
- ISBN 9781584885603
- Weight: 524g
- Dimensions: 156 x 234mm
- Publication Date: 01 Nov 2005
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Hardback
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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.\
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.
