Classical Topics in Complex Function Theory

Book Details :
Title : Classical Topics in Complex Function Theory (Graduate Texts in Mathematics).
Author : Reinhold Remmert, L.D. Kay.
Paperback : 380 pages
Publisher : Springer; Softcover reprint of hardcover 1st ed. 1997 edition (December 1, 2010).
Language : English.
ISBN-10 : 1441931147.
ISBN-13 : 978-1441931146.
Size : 22.6 MB.
Type : Pdf.
Book Description : This book is an ideal text for an advanced course in the theory of complex functions. The author successfully enables the reader to experience function theory personally and to participate in the work of the creative mathematician. Unlike the first volume, it contains numerous glimpses of the function theory of several complex variables emphasizing how autonomous this discipline has become. Covered are Weierstrass’ product theorem, Mittag-Leffler’s theorem, the Riemann mapping theorem, and Runge’s theorems on approximations of analytic functions. Remmert elegantly breaks the material down into small intelligible sections, with perfectly compact proofs and historical comments interwoven throughout the text. The abundance of examples, exercises, historical remarks (e.g. Gauss’ review of Riemann’s thesis), and an extensive list of references will make this book an invaluable source. An ideal text for an advanced course in the theory of complex functions, this book leads readers to experience function theory personally and to participate in the work of the creative mathematician. The author includes numerous glimpses of the function theory of several complex variables, which illustrate how autonomous this discipline has become. In addition to standard topics, readers will find Eisenstein’s proof of Euler’s product formula for the sine function; Wielandts uniqueness theorem for the gamma function; Stirlings formula; Isssas theorem; Besses proof that all domains in C are domains of holomorphy; Wedderburns lemma and the ideal theory of rings of holomorphic functions; Estermanns proofs of the overconvergence theorem and Blochs theorem; a holomorphic imbedding of the unit disc in C3; and Gausss expert opinion on Riemanns dissertation. Remmert elegantly presents the material in short clear sections, with compact proofs and historical comments interwoven throughout the text. The abundance of examples, exercises, and historical remarks, as well as the extensive bibliography, combine to make an invaluable source for students and teachers alike.

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