Derivatives of Inner Functions (eBook, PDF) - Mashreghi, Javad
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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…mehr

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Produktbeschreibung
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.
Rezensionen
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)