Fractional Cauchy Transforms

Informationen zum Autor 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. Klappentext 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 with numerous references! 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. Discussions include radial limits! exceptional sets! zeros! factorization! and the relations between fractional Cauchy transforms and Dirichlet and Besov spaces . Zusammenfassung Focuses on concrete analytic questions, with functional analysis providing the general framework. This work features discussions including radial limits, exceptional sets, zeros, factorization, and the relations between fractional Cauchy transforms and Dirichlet and Besov spaces. Inhaltsverzeichnis INTRODUCTIONDefinition of the families FaRelations between F1and H1 The Riesz-Herglotz formula Representations with real measures and h1 The F. and M. Riesz theoremThe representing measures for functions in F1The one-to-one correspondence between measures and functions in the Riesz-Herglotz formulaThe Banach space structure of FaNorm convergence and convergence uniform on compact setsNotes BASIC PROPERTIES OF Fa oProperties of the gamma function and the binomial coefficientsA product theorem Membership of f and f ' in FaThe inclusion of Fa in Fb when 0 = a

Product details

• Authors: Rita A. Hibschweiler, Rita A. (University of New Hampshire Hibschweiler, Rita A. Macgregor Hibschweiler, Hibschweiler Rita A., Thomas H. MacGregor, Thomas H. (Pemaquid MacGregor, MacGregor Thomas H., B.l. Macgregor Tembe
• Assisted by: Rita A. Hibschweiler (Editor), Thomas H. MacGregor (Editor), B.L. Tembe (Editor), Haim Brezis (Editor of the series), Ronald G. Douglas (Editor of the series), Alan Jeffrey (Editor of the series)
• Publisher: Taylor & Francis Ltd.
• Languages: English
• Product format: Hardback
• Released: 01.11.2005
• EAN: 9781584885603
• ISBN: 978-1-58488-560-3
• No. of pages: 268
• Series: Monographs and Surveys in Pure and Applied Mathematics; Monographs and Surveys in Pure and Applied Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; MATHEMATICS / Functional Analysis, Functional analysis & transforms, Functional analysis and transforms