Distortion Theorems in Relation to Linear Integral Operators - Hardcover

by Yusaku Komatu (Author), Yusaku Komatsu (Author), Y. Komatu (Author)

Preface. 0. Introduction. Part I: Integral Operators. 1. Basic Integral Operators. 2. Properties of Integral Operators. 3. Applications. Part II: Distortion Theorems. 4. Distortions on Univalent Functions. 5. Distortions on Real Part. 6. Distortions on Miscellaneous Functionals. References. Index of Names. Index of Topics.

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This book represents over twenty years of research on distortions of functionals under actions of linear integral operators. It is divided into two parts. The first part addresses linear integral operators, establishing their properties and attempting to arrive at both specialisations as well as generalisations to be used in the second part. The second part is devoted mainly to the development of several kinds of distortions under actions of integral operators for various familiar functionals. Among the topics that are treated are absolute modulus, real part, range, length and area, angular derivative, etc. Also, distortions on the class of univalent functions and its subclasses, Caratheodory class, and distortions by a differential operator are dealt with. This volume will be of interest to researchers and graduate students whose work involves complex analysis, integral transforms, operational calculus and operator theory. The volume is self-contained, giving many proofs, and is suitable for private study as well as for seminars.