Convolutions in geometric function theory : notes du cours à la vingtième session du Séminaire de mathématiques supérieures/séminaire scientifique OTAN; Montréal, 3-21 août 1981

This book is an introduction to the theory of entire and meromorphic functions intended for advanced graduate students in mathematics and for professional mathematicians. The book provides a clear treatment of the Nevanlinna theory of value distribution of meromorphic functions, and presentation of the Rubel-Taylor Fourier Series method for meromorphic functions and the Miles theorem on efficient quotient representation. It has a concise but complete treatment of the Polya theory of the Borel transform and the conjugate indicator diagram. It contains some of Buck's results on integer-valued entire functions, and closes with the Malliavin-Rubel uniqueness theorem. The approach gets to the heart of the matter without excessive scholarly detours. It prepares the reader for further study of the vast literature on the subject, which is one of the cornerstones of complex analysis Contents......Page all_19458_to_00166.cpc0005.djvu Introduction......Page all_19458_to_00166.cpc0007.djvu 1.1 The duality principle......Page all_19458_to_00166.cpc0011.djvu 1.2 Test sets......Page all_19458_to_00166.cpc0015.djvu 1.3 Special cases (1)......Page all_19458_to_00166.cpc0018.djvu 1.4 Special cases (2)......Page all_19458_to_00166.cpc0024.djvu 1.5 Convolution invariance......Page all_19458_to_00166.cpc0031.djvu 1.6 Additional information......Page all_19458_to_00166.cpc0037.djvu 2.1 Introductory remarks......Page all_19458_to_00166.cpc0041.djvu 2.2 Prestarlike functions......Page all_19458_to_00166.cpc0044.djvu 2.3 Application to close-to-convex and related functions......Page all_19458_to_00166.cpc0059.djvu 2.4 Related criteria for univalence......Page all_19458_to_00166.cpc0066.djvu 2.5 M and related classes of univalent functions......Page all_19458_to_00166.cpc0071.djvu 2.6 Convex subordination......Page all_19458_to_00166.cpc0080.djvu 2.7 Univalence criteria via convolution and applications......Page all_19458_to_00166.cpc0090.djvu 2.8 Additional information......Page all_19458_to_00166.cpc0093.djvu 3.1 Some more duality theory......Page all_19458_to_00166.cpc0101.djvu 3.2 Special cases......Page all_19458_to_00166.cpc0108.djvu 3.3 Additional information......Page all_19458_to_00166.cpc0114.djvu 4.1 Bound and hull preserving operators......Page all_19458_to_00166.cpc0117.djvu 4.2 Application to univalent functions......Page all_19458_to_00166.cpc0126.djvu 4.3 Polynomials nonvanishing in the unit disc......Page all_19458_to_00166.cpc0132.djvu 4.4 An extension of Szegõ's theorem......Page all_19458_to_00166.cpc0138.djvu 4.5 Additional information......Page all_19458_to_00166.cpc0139.djvu 5.1 Connection with convolutions......Page all_19458_to_00166.cpc0143.djvu 5.2 Univalent solutions......Page all_19458_to_00166.cpc0146.djvu 5.3 Extension of Schwarz' Lemma......Page all_19458_to_00166.cpc0152.djvu 5.4 Additional remarks......Page all_19458_to_00166.cpc0154.djvu References......Page all_19458_to_00166.cpc0155.djvu Subject Index......Page all_19458_to_00166.cpc0165.djvu List of Symbols and Abbreviations......Page all_19458_to_00166.cpc0166.djvu Stephan Ruscheweyh. At Head Of Title: Séminaire De Mathématiques Supérieures, Seminaire Scientifique Otan (nato Advanced Study Institute), Département De Mathématiques Et De Statistique--université De Montréal. Includes Index. Bibliography: P. [157]-166.