Explorations in Complex Functions: 287 (Graduate Texts in Mathematics, 287) - Image 1

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Springer Explorations in Complex Functions: 287 (Graduate Texts in Mathematics, 287)

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Complex Analysis

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Description

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 riseto 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.

Product Specifications

Brand: Springer
Format: hardcover
ASIN: 3030545326
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Analysis > Complex Analysis
Domain: Amazon UK
Release Date: 20 October 2020
Listed Since: 20 June 2020

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Springer Explorations in Complex Functions: 287 (Graduate Texts in Mathematics, 287)

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