國立虎尾科技大學 |

Explorations in Complex Functions

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Explorations in Complex Functions/ by Richard Beals, Roderick S. C. Wong.
Author:	Beals, Richard.
other author:	Wong, Roderick S. C.
Description:	XVI, 353 p. 30 illus., 29 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Functions of complex variables. -
Online resource:	https://doi.org/10.1007/978-3-030-54533-8
ISBN:	9783030545338

Explorations in Complex Functions
Beals, Richard.

Explorations in Complex Functions[electronic resource] /by Richard Beals, Roderick S. C. Wong. - 1st ed. 2020. - XVI, 353 p. 30 illus., 29 illus. in color.online resource. - Graduate Texts in Mathematics,2870072-5285 ;. - Graduate Texts in Mathematics,222.

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.

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.

ISBN: 9783030545338

Standard No.: 10.1007/978-3-030-54533-8doiSubjects--Topical Terms:

528649
Functions of complex variables.

LC Class. No.: QA331-355

Dewey Class. No.: 515.9

Explorations in Complex Functions
LDR:03765nam a22004095i 4500 001 1017661
003 DE-He213
005 20201019132823.0
007 cr nn 008mamaa
008 210318s2020 gw | s |||| 0|eng d
020 $a 9783030545338 $9 978-3-030-54533-8
024 7 $a 10.1007/978-3-030-54533-8 $2 doi
035 $a 978-3-030-54533-8
050 4 $a QA331-355
072 7 $a PBKD $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKD $2 thema
082 0 4 $a 515.9 $2 23
100 1 $a Beals, Richard. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 686507
245 1 0 $a Explorations in Complex Functions $h [electronic resource] / $c by Richard Beals, Roderick S. C. Wong.
250 $a 1st ed. 2020.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a XVI, 353 p. 30 illus., 29 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Graduate Texts in Mathematics, $x 0072-5285 ; $v 287
505 0 $a 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.
520 $a 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.
650 0 $a Functions of complex variables. $3 528649
650 0 $a Special functions. $3 1257411
650 0 $a Number theory. $3 527883
650 1 4 $a Functions of a Complex Variable. $3 672126
650 2 4 $a Special Functions. $3 672152
650 2 4 $a Number Theory. $3 672023
700 1 $a Wong, Roderick S. C. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1312524
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030545321
776 0 8 $i Printed edition: $z 9783030545345
776 0 8 $i Printed edition: $z 9783030545352
830 0 $a Graduate Texts in Mathematics, $x 0072-5285 ; $v 222 $3 1254915
856 4 0 $u https://doi.org/10.1007/978-3-030-54533-8
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)