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Explorations in Complex Functions

Book on DemandKartoniert, Paperback
353 Seiten
Englisch
Springererschienen am21.10.20211st ed. 2020
Readers interested in complex analysis will appreciate the unique combination of topics and connections collected in this book. Beginning with a review of the main tools of complex analysis, harmonic analysis, and functional analysis, the authors go on to present multiple different, self-contained avenues to proceed.mehr
Verfügbare Formate
BuchGebunden
EUR35,30
Book on DemandKartoniert, Paperback
EUR26,74

Produkt

KlappentextReaders interested in complex analysis will appreciate the unique combination of topics and connections collected in this book. Beginning with a review of the main tools of complex analysis, harmonic analysis, and functional analysis, the authors go on to present multiple different, self-contained avenues to proceed.
Zusammenfassung
Illustrates a unique, accessible range of topics relevant across analysis and number theory

Includes pathways toward applications of the Schwarzian, the Riemann hypothesis, and parametrization of Riemann surfaces

Offers many self-contained options for exploring topics relevant to specific interests

Enhances the theory with ample exercises and color illustrations throughout

Includes supplementary material: sn.pub/extras
Details
ISBN/GTIN978-3-030-54535-2
ProduktartBook on Demand
EinbandartKartoniert, Paperback
Verlag
Erscheinungsjahr2021
Erscheinungsdatum21.10.2021
Auflage1st ed. 2020
ReiheGraduate Texts in Mathematics
Seiten353 Seiten
SpracheEnglisch
IllustrationenXVI, 353 p. 30 illus., 29 illus. in color.
Artikel-Nr.50117120

Inhalt/Kritik

Inhaltsverzeichnis
Basics.- Linear Fractional Transformations.- Hyperbolic geometry.- Harmonic Functions.- Conformal maps and the Riemann mapping theorem.- The Schwarzian derivative.- Riemann surfaces and algebraic curves.- Entire functions.- Value distribution theory.- The gamma and beta functions.- The Riemann zeta function.- L-functions and primes.- The Riemann hypothesis.- Elliptic functions and theta functions.- Jacobi elliptic functions.- Weierstrass elliptic functions.- Automorphic functions and Picard's theorem.- Integral transforms.- Theorems of Phragmén-Lindelöf and Paley-Wiener.- Theorems of Wiener and Lévy; the Wiener-Hopf method.- Tauberian theorems.- Asymptotics and the method of steepest descent.- Complex interpolation and the Riesz-Thorin theorem.mehr
Kritik
"This is a suitable book with a proper concept at the right time. It is suitable because it shows the beauty, power and profundity of complex analysis, enlightens how many sided it is with all its inspirations and cross-connections to other branches of mathematics." (Heinrich Begehr, zbMATH 1460.30001, 2021)mehr

Schlagworte

Autor

Richard Beals is Professor Emeritus of Mathematics at Yale University. His research interests include ordinary and partial differential equations, operator theory, integrable systems, and transport theory. He has authored many books, including Advanced Mathematical Analysis, published in 1973 as the twelfth volume in the series Graduate Texts in Mathematics.

Roderick S. C. Wong is Professor Emeritus of Mathematics at the City University of Hong Kong. His research interests include asymptotic analysis, perturbation methods, and special functions. He has been president of the Canadian Applied Mathematics Society and the Hong Kong Mathematical Society, and received numerous professional honors, including election to the European Academy of Sciences in 2007. He has written and edited a wide variety of books, with several notable works in the area of special functions.

This is the third book in the authors' collaboration, after two previous volumeson special functions.