Normal Families and Normal Functions
Normal Families and Normal Functions

Author: Peter V. Dovbush

Publisher: CRC Press

Published: 2024-02-27

Total Pages: 269

ISBN-13: 1003849857

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This book centers on normal families of holomorphic and meromorphic functions and also normal functions. The authors treat one complex variable, several complex variables, and infinitely many complex variables (i.e., Hilbert space). The theory of normal families is more than 100 years old. It has played a seminal role in the function theory of complex variables. It was used in the first rigorous proof of the Riemann mapping theorem. It is used to study automorphism groups of domains, geometric analysis, and partial differential equations. The theory of normal families led to the idea, in 1957, of normal functions as developed by Lehto and Virtanen. This is the natural class of functions for treating the Lindelof principle. The latter is a key idea in the boundary behavior of holomorphic functions. This book treats normal families, normal functions, the Lindelof principle, and other related ideas. Both the analytic and the geometric approaches to the subject area are offered. The authors include many incisive examples. The book could be used as the text for a graduate research seminar. It would also be useful reading for established researchers and for budding complex analysts.

Normal Families
Normal Families

Author: Joel L. Schiff

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 241

ISBN-13: 1461209072

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A book on the subject of normal families more than sixty years after the publication of Montel's treatise Ler;ons sur les familles normales de fonc tions analytiques et leurs applications is certainly long overdue. But, in a sense, it is almost premature, as so much contemporary work is still being produced. To misquote Dickens, this is the best of times, this is the worst of times. The intervening years have seen developments on a broad front, many of which are taken up in this volume. A unified treatment of the classical theory is also presented, with some attempt made to preserve its classical flavour. Since its inception early this century the notion of a normal family has played a central role in the development of complex function theory. In fact, it is a concept lying at the very heart of the subject, weaving a line of thought through Picard's theorems, Schottky's theorem, and the Riemann mapping theorem, to many modern results on meromorphic functions via the Bloch principle. It is this latter that has provided considerable impetus over the years to the study of normal families, and continues to serve as a guiding hand to future work. Basically, it asserts that a family of analytic (meromorphic) functions defined by a particular property, P, is likely to be a normal family if an entire (meromorphic in

Normal Families Of Meromorphic Functions
Normal Families Of Meromorphic Functions

Author: Qitai Zhuang

Publisher: World Scientific

Published: 1993-04-27

Total Pages: 488

ISBN-13: 9814504629

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This book presents in a clear and systematic manner the general theory of normal families, quasi-normal families and Qm-normal families of meromorphic functions, and various applications. Much of this book contains results of the author's research, among them is the notion of Qm-normality which includes the classical notions of normality and quasi-normality introduced by Montel as particular cases. In this book, the notion of closed families of meromorphic functions is also introduced. In addition, applications concerning the existence of the solution of various extremal problems for certain classes of univalent or multivalent functions can also be found.

Nevanlinna Theory, Normal Families, and Algebraic Differential Equations
Nevanlinna Theory, Normal Families, and Algebraic Differential Equations

Author: Norbert Steinmetz

Publisher: Springer

Published: 2017-07-24

Total Pages: 249

ISBN-13: 3319598007

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This book offers a modern introduction to Nevanlinna theory and its intricate relation to the theory of normal families, algebraic functions, asymptotic series, and algebraic differential equations. Following a comprehensive treatment of Nevanlinna’s theory of value distribution, the author presents advances made since Hayman’s work on the value distribution of differential polynomials and illustrates how value- and pair-sharing problems are linked to algebraic curves and Briot–Bouquet differential equations. In addition to discussing classical applications of Nevanlinna theory, the book outlines state-of-the-art research, such as the effect of the Yosida and Zalcman–Pang method of re-scaling to algebraic differential equations, and presents the Painlevé–Yosida theorem, which relates Painlevé transcendents and solutions to selected 2D Hamiltonian systems to certain Yosida classes of meromorphic functions. Aimed at graduate students interested in recent developments in the field and researchers working on related problems, Nevanlinna Theory, Normal Families, and Algebraic Differential Equations will also be of interest to complex analysts looking for an introduction to various topics in the subject area. With examples, exercises and proofs seamlessly intertwined with the body of the text, this book is particularly suitable for the more advanced reader.

A Nearly Normal Family
A Nearly Normal Family

Author: M. T. Edvardsson

Publisher: Celadon Books

Published: 2019-06-25

Total Pages: 361

ISBN-13: 1250204429

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Now a Netflix Limited Series "...A compulsively readable tour de force." —The Wall Street Journal New York Times Book Review recommends M.T. Edvardsson’s A Nearly Normal Family and lauds it as a “page-turner” that forces the reader to confront “the compromises we make with ourselves to be the people we believe our beloveds expect.” (NYTimes Book Review Summer Reading Issue) M.T. Edvardsson’s A Nearly Normal Family is a gripping legal thriller that forces the reader to consider: How far would you go to protect the ones you love? In this twisted narrative of love and murder, a horrific crime makes a seemingly normal family question everything they thought they knew about their life—and one another. Eighteen-year-old Stella Sandell stands accused of the brutal murder of a man almost fifteen years her senior. She is an ordinary teenager from an upstanding local family. What reason could she have to know a shady businessman, let alone to kill him? Stella’s father, a pastor, and mother, a criminal defense attorney, find their moral compasses tested as they defend their daughter, while struggling to understand why she is a suspect. Told in an unusual three-part structure, A Nearly Normal Family asks the questions: How well do you know your own children? How far would you go to protect them?

Normal Family
Normal Family

Author: Chrysta Bilton

Publisher: Hachette UK

Published: 2022-07-12

Total Pages: 317

ISBN-13: 0316536520

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This riveting, nuanced memoir about unforgettable individuals thrown together by chance and DNA tells a story of nature, nurture, and coming to terms with one's true inheritance. What is a “normal family,” and how do you go about making one? Chrysta Bilton’s magnetic, larger-than-life mother, Debra, yearned to have a child, but as a single gay woman in 1980s California, she had few options. Until one day, while getting her hair done in a Beverly Hills salon, she met a man and instantly knew he was the one she’d been looking for. Beautiful, athletic, artistic, and from a well-to-do family, Jeffrey Harrison appeared to be Debra’s ideal sperm donor. A verbal agreement, a couple of thousand in cash, and a few squirts of a turkey baster later, and Chrysta was conceived. Over the years, Jeffrey would make regular appearances at the family home, which grew to include Chrysta’s baby sister. But how much did Debra really know about the man she’d chosen to father her daughters? And as a single mother torn between ferocious independence and abject dependence—on other women, alcohol, drugs, and the adrenaline of get-rich-quick schemes—what secrets of her own was she keeping? It wasn’t until Chrysta was a young adult that she discovered just how much her parents had hidden from their daughters—and each other—including a shocking revelation with far-reaching consequences not only for Debra, Chrysta, and her sister, but for dozens and possibly hundreds of unsuspecting families across the country. After a lifetime of longing for a “normal family,” can Chrysta face the reality of her own, in all its complexity? Bringing us into the fold of a deeply dysfunctional yet fiercely loving clan that is anything but “normal,” this emotional roller coaster of a memoir will make you cry, laugh, and rethink the meaning of family. Named a 'Best Book of the Summer' by LA Times, People, USA Today, Vanity Fair, The Hollywood Reporter, Amazon, Apple, Cup of Jo, Kirkus, Parade, & Today

Iteration of Rational Functions
Iteration of Rational Functions

Author: Alan F. Beardon

Publisher: Springer Science & Business Media

Published: 2000-09-27

Total Pages: 308

ISBN-13: 9780387951515

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This book focuses on complex analytic dynamics, which dates from 1916 and is currently attracting considerable interest. The text provides a comprehensive, well-organized treatment of the foundations of the theory of iteration of rational functions of a complex variable. The coverage extends from early memoirs of Fatou and Julia to important recent results and methods of Sullivan and Shishikura. Many details of the proofs have not appeared in print before.

The Multivariate Normal Distribution
The Multivariate Normal Distribution

Author: Y.L. Tong

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 281

ISBN-13: 1461396557

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The multivariate normal distribution has played a predominant role in the historical development of statistical theory, and has made its appearance in various areas of applications. Although many of the results concerning the multivariate normal distribution are classical, there are important new results which have been reported recently in the literature but cannot be found in most books on multivariate analysis. These results are often obtained by showing that the multivariate normal density function belongs to certain large families of density functions. Thus, useful properties of such families immedi ately hold for the multivariate normal distribution. This book attempts to provide a comprehensive and coherent treatment of the classical and new results related to the multivariate normal distribution. The material is organized in a unified modern approach, and the main themes are dependence, probability inequalities, and their roles in theory and applica tions. Some general properties of a multivariate normal density function are discussed, and results that follow from these properties are reviewed exten sively. The coverage is, to some extent, a matter of taste and is not intended to be exhaustive, thus more attention is focused on a systematic presentation of results rather than on a complete listing of them.

The Skew-Normal and Related Families
The Skew-Normal and Related Families

Author: Adelchi Azzalini

Publisher: Cambridge University Press

Published: 2014

Total Pages: 271

ISBN-13: 1107029279

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The standard resource for statisticians and applied researchers. Accessible to the wide range of researchers who use statistical modelling techniques.