Explorations in Complex Functions

Name: Explorations in Complex Functions
Brand: Springer Nature Switzerland AG
SKU: 9783030545352
Price: 42.8 EUR
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Автор: Richard Beals, Roderick S. C. Wong

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Корици: С меки корици

Издател: Springer Nature Switzerland AG

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This textbook explores a selection of topics in complex analysis. From core material in the mainstre...

Информация за книгата

Автор

Richard Beals, Roderick S. C. Wong

Език

Английски език

Корици

Книга - С меки корици

Издадена

2021

страници

353

EAN

9783030545352

ISBN

3030545350

Enbook ID

38417881

Издател

Springer Nature Switzerland AG

Теглоt

672

Размери

155 x 235

Пълно описание

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.

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