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

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?

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

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.

Growing up, they didn't believe they had a future. Together, they are building forever. Alexis Black persevered through her mother's death and her father's imprisonment. And after escaping a long and abusive relationship, the college junior promised her foster parents not to date for at least a year. But when she meets an incoming freshman on the first day of their scholarship program, she feels the world melt away, as though it were only the two of them in the room. Justin Black lived in the poorest section of Detroit before his parents surrendered him to the foster care system at the age of nine. But when he grabs the chance for better opportunities by pursuing higher education, he can't help but be drawn to a beautiful third-year student. At first, their past traumas--and their age difference--conspired to complicate their attraction. But the joy each took in the other and eventually conquered those obstacles, and these two survivors journeyed together toward healing. In a stark and wholehearted true story that shares how two individuals on separate paths found each other, Alexis and Justin merge their course into one full of hope and purpose. And hand-in-hand, with a desire to help others, they learned to reject the abusive patterns of their past, thereby intentionally breaking the cycle of generational violence and unhealthy behaviors. Written in an engaging novelistic style, the authors put forward a thoughtful exchange of ideas and personal experiences illustrating how anybody, no matter their backgrounds, can have a life of self-empowerment and joy. Broken down into four sections that cover crucial topics such as "Worthiness" and "Mental Health," this compelling narrative will help any who are learning to love themselves and want to end the line of toxic relationships. Redefining Normal: How Two Foster Kids Beat The Odds and Discovered Healing, Happiness, and Love is a page-turning memoir that will open your eyes to possibilities and dreams. If you like honest tales of triumph, refreshing transparency, and resilient faith in God, then you'll adore Justin and Alexis' inspirational story. This story contains mentions of domestic violence, trauma, sexual assault, and other difficult issues faced on the road to healing. Buy Redefining Normal to claim victory over harmful pasts today!

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.

From the author of Why Dogs Are Better Than Men comes a sly and devastatingly funny look at love and family relationships in the age of therapy. Features cartoons plus a bonus short story.