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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.
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.
Roderick S. C. Wong is Professor Emeritus of Mathematics at the City University of Hong Kong. His research interests include asymptotic analysis, perturbation methods, and special functions. He has been president of the Canadian Applied Mathematics Society and the Hong Kong Mathematical Society, and received numerous professional honors, including election to the European Academy of Sciences in 2007. He has written and edited a wide variety of books, with several notable works in the area of special functions.
This is the third book in the authors' collaboration, after two previous volumeson special functions.
Illustrates a unique, accessible range of topics relevant across analysis and number theory
Includes pathways toward applications of the Schwarzian, the Riemann hypothesis, and parametrization of Riemann surfaces
Offers many self-contained options for exploring topics relevant to specific interests
Enhances the theory with ample exercises and color illustrations throughout
Includes supplementary material: [...]
| Erscheinungsjahr: | 2020 |
|---|---|
| Fachbereich: | Analysis |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 372 |
| Reihe: | Graduate Texts in Mathematics |
| Inhalt: |
xvi
353 S. 1 s/w Illustr. 29 farbige Illustr. 353 p. 30 illus. 29 illus. in color. |
| ISBN-13: | 9783030545321 |
| ISBN-10: | 3030545326 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: |
Wong, Roderick S. C.
Beals, Richard |
| Auflage: | 1st ed. 2020 |
| Hersteller: |
Springer International Publishing
Graduate Texts in Mathematics |
| Maße: | 241 x 160 x 25 mm |
| Von/Mit: | Roderick S. C. Wong (u. a.) |
| Erscheinungsdatum: | 20.10.2020 |
| Gewicht: | 0,79 kg |
Roderick S. C. Wong is Professor Emeritus of Mathematics at the City University of Hong Kong. His research interests include asymptotic analysis, perturbation methods, and special functions. He has been president of the Canadian Applied Mathematics Society and the Hong Kong Mathematical Society, and received numerous professional honors, including election to the European Academy of Sciences in 2007. He has written and edited a wide variety of books, with several notable works in the area of special functions.
This is the third book in the authors' collaboration, after two previous volumeson special functions.
Illustrates a unique, accessible range of topics relevant across analysis and number theory
Includes pathways toward applications of the Schwarzian, the Riemann hypothesis, and parametrization of Riemann surfaces
Offers many self-contained options for exploring topics relevant to specific interests
Enhances the theory with ample exercises and color illustrations throughout
Includes supplementary material: [...]
| Erscheinungsjahr: | 2020 |
|---|---|
| Fachbereich: | Analysis |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 372 |
| Reihe: | Graduate Texts in Mathematics |
| Inhalt: |
xvi
353 S. 1 s/w Illustr. 29 farbige Illustr. 353 p. 30 illus. 29 illus. in color. |
| ISBN-13: | 9783030545321 |
| ISBN-10: | 3030545326 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: |
Wong, Roderick S. C.
Beals, Richard |
| Auflage: | 1st ed. 2020 |
| Hersteller: |
Springer International Publishing
Graduate Texts in Mathematics |
| Maße: | 241 x 160 x 25 mm |
| Von/Mit: | Roderick S. C. Wong (u. a.) |
| Erscheinungsdatum: | 20.10.2020 |
| Gewicht: | 0,79 kg |
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