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Explorations in complex functions / Richard Beals and Roderick S. C. Wong.
Author
Beals, Richard, 1938-
[Browse]
Format
Book
Language
English
Εdition
1st ed. 2020.
Published/Created
Cham, Switzerland : Springer, [2020]
©2020
Description
1 online resource (XVI, 353 p. 30 illus., 29 illus. in color.)
Availability
Available Online
Springer Nature - Springer Mathematics and Statistics eBooks 2020 English International
Details
Subject(s)
Functions of complex variables
[Browse]
Mathematical analysis
[Browse]
Functions, Special
[Browse]
Author
Wong, Roderick, 1944-
[Browse]
Series
Graduate Texts in Mathematics, 287
[More in this series]
Graduate Texts in Mathematics, 0072-5285 ; 287
[More in this series]
Summary note
This textbook explores a selection of topics in complex analysis. From core material in the mainstream of complex analysis itself, to tools that are widely used in other areas of mathematics, this versatile compilation offers a selection of many different paths. 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. Chapters on linear fractional transformations, harmonic functions, and elliptic functions offer pathways to hyperbolic geometry, automorphic functions, and an intuitive introduction to the Schwarzian derivative. The gamma, beta, and zeta functions lead into L-functions, while a chapter on entire functions opens pathways to the Riemann hypothesis and Nevanlinna theory. Cauchy transforms give rise to Hilbert and Fourier transforms, with an emphasis on the connection to complex analysis. Valuable additional topics include Riemann surfaces, steepest descent, tauberian theorems, and the Wiener–Hopf method. Showcasing an array of accessible excursions, Explorations in Complex Functions is an ideal companion for graduate students and researchers in analysis and number theory. Instructors will appreciate the many options for constructing a second course in complex analysis that builds on a first course prerequisite; exercises complement the results throughout.
Bibliographic references
Includes bibliographical references and index.
Source of description
Description based on print version record.
Language note
English
Contents
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.
Show 20 more Contents items
ISBN
3-030-54533-4
OCLC
1202754286
Doi
10.1007/978-3-030-54533-8
Statement on language in description
Princeton University Library aims to describe library materials in a manner that is respectful to the individuals and communities who create, use, and are represented in the collections we manage.
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Explorations in complex functions / Richard Beals, Roderick S.C. Wong.
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