Derivatives of Inner Functions
1st Edition
Published on 14. November 2012
X, 170 pages
978-1-4614-5611-7 (ISBN)
Description
Inner functions form an important subclass of bounded analytic functions. Since they have unimodular boundary values, they appear in many extremal problems of complex analysis. They have been extensively studied since early last century, and the literature on this topic is vast. Therefore, this book is devoted to a concise study of derivatives of these objects, and confined to treating the integral means of derivatives and presenting a comprehensive list of results on Hardy and Bergman means. The goal is to provide rapid access to the frontiers of research in this field. This monograph will allow researchers to get acquainted with essentials on inner functions, and it is self-contained, which makes it accessible to graduate students.
Reviews / Votes
From the reviews:
"This short monograph presents an account with full proofs of early investigations from around 1970-1980 on derivatives of inner functions . . the author also revisits Carathéodory's theory on angular derivatives and gives a brief glimpse on Frostman's results on exceptional sets for inner functions. . It fits well for student seminars." (Raymond Mortini, Mathematical Reviews, August, 2013)More details
Series
Language
English
Place of publication
New York
United States
Publishing group
Springer US
Target group
Professional and scholarly
Product notice
Reflowable
Illustrations
X, 170 p.
File size
1,94 MB
ISBN-13
978-1-4614-5611-7 (9781461456117)
DOI
10.1007/978-1-4614-5611-7
Schweitzer Classification
Other editions
Additional editions
Content
.-Preface.-1. Inner Functions.-2. The Exceptional Set of an Inner Function.-3. The Derivative of Finite Blaschke Products.-4. Angular Derivative.-5. Hp-Means of S'.-6. Bp-Means of S'.-7. The Derivative of a Blaschke Product.-8. Hp-Means of B'.-9. Bp-Means of B'.-10. The Growth of Integral Means of B'.-References.-Index.
