000			02988 a2200385 4500
003			NISER
005			20260109102433.0
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020			_a9783030545352 _qPaperback
040			_aNISER LIBRARY _beng _cNISER LIBRARY
082	0	4	_a517.53 _bBEA-E
100	1		_aBeals, Richard
245	1	0	_aExplorations in complex functions
260			_aCham, Switzerland : _bSpringer, _c2020.
300			_axvi, 353 pages : _billustrations (1 b/w illustrations, 29 illustrations in colour) ; _c23 cm.
490			_aGraduate Texts in Mathematics, _v287 _x0072-5285 ;
504			_aIncludes bibliographical references and index.
520			_aThis 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 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.
650		0	_aFunctions of complex variables
650		0	_aMathematical analysis
650		0	_aFunctions, Special
650		0	_aNevanlinna theory
650		0	_aCauchy transform
650		0	_aHilbert transform
650		0	_aFourier transform
650		0	_aRiemann hypothesis complex analysis
650		0	_aAutomorphic functions
650		0	_aHyperbolic geometry
650		0	_aSchwarzian derivative
650		0	_aLinear fractional transformations
700	1		_aWong, Roderick S. C.
856	4	1	_3Table of contents _uhttps://link.springer.com/content/pdf/bfm:978-3-030-54533-8/1
856	4	1	_3Reviews _uhttps://www.goodreads.com/book/show/54211121-explorations-in-complex-functions?ref=nav_sb_ss_1_33#CommunityReviews
942			_cBK _2udc
999			_c36731 _d36731