1st Edition
Fractional Cauchy Transforms
268 Pages
50 B/W Illustrations
by
Chapman & Hall
272 Pages
by
Chapman & Hall
Also available as eBook on:
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... Read more
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
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
Biography
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.
