| Dewey Class |
515.9 |
| Titel |
Explorations in Complex Functions ([EBook]) / by Richard Beals, Roderick S. C. Wong. |
| Verfasser |
Beals, Richard. , 1938- |
| Added Personal Name |
Wong, Roderick S. C. |
| Other name(s) |
SpringerLink (Online service) |
| Edition statement |
1st ed. 2020. |
| Veröffentl |
Cham : Springer International Publishing , 2020. |
| Physical Details |
XVI, 353 pages: 30 illus., 29 illus. in color. : online resource. |
| Reihe |
Graduate texts in mathematics 0072-5285 ; ; 287 |
| ISBN |
9783030545338 |
| 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.: |
| Contents note |
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. |
| Mode of acces to digital resource |
Digital book. Cham Springer Nature 2020. - Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users). |
| Internet Site |
https://doi.org/10.1007/978-3-030-54533-8 |
| LINKS ZU 'VERWANDTEN WERKEN |
Schlagwörter: .
Functions of a Complex Variable .
Functions of complex variables .
Number Theory .
Special Functions .
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