
Derivatives of Inner Functions
Javad Mashreghi(Author)
Springer (Publisher)
Published on 14. November 2012
Book
Hardback
X, 170 pages
978-1-4614-5610-0 (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
Edition
2013 ed.
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Research
Illustrations
X, 170 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 13 mm
Weight
442 gr
ISBN-13
978-1-4614-5610-0 (9781461456100)
DOI
10.1007/978-1-4614-5611-7
Schweitzer Classification
Other editions
Additional editions


Javad Mashreghi
Derivatives of Inner Functions
E-Book
11/2012
1st Edition
Springer
€53.49
Available for download
Person
Javad Mashreghi is an esteemed mathematician and author renowned for his work in the areas of functional analysis, operator theory, and complex analysis. He has made significant contributions to the study of analytic function spaces and the operators that act upon them. Prof. Mashreghi has held various prestigious positions throughout his career. He served as the 35th President of the Canadian Mathematical Society (CMS) and has been recognized as a Lifetime Fellow of both CMS and the Fields Institute. He currently holds the Canada Research Chair at Université Laval and has also been honored as a Fulbright Research Chair at Vanderbilt University.
Le Hai Khoi is an expert in the fields of function spaces and operator theory, with a particular focus on the representation of functions using series expansions involving exponential functions, rational functions, and Dirichlet series. He has made significant contributions to these areas and has a prolific research output, having published over 80 research papers in the relevant field. Prof. Le Hai Khoi is well-known for his expertise and active involvement in the study of $\mathcal{N}_p$ spaces, which are Banach and Hilbert spaces of analytic functions on the open unit disk and open unit ball.
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.