Explorations in Complex Functions

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Explorations in Complex Functions
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Format:
Bog, hardback
Udgivelsesdato:
20-10-2020
Sprog:
Engelsk
Udgave:
1st ed. 2020.

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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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Udgivelsesdato:
20-10-2020
ISBN13:
9783030545321
Vægt:
771 g
Bredde:
155 mm
Højde:
235 mm
Nummer i serien:
287
Format:
Hardback
Forfattere
Bibliotekernes beskrivelse 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. 1 Hardback 30 Tables, color; 29 Illustrations, color; 1 Illustrations, black and white; XVI, 353 p. 30 illus., 29 illus. in color.

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