000			a
999			_c32437 _d32437
008			230831b xxu||||| |||| 00| 0 eng d
020			_a9783030545352
082			_a515.9 _bBEA
100			_aBeals, Richard
245			_aExplorations in complex functions
260			_bSpringer, _c2020 _aCham :
300			_axvi, 353 p. ; _bill., _c24 cm
365			_b49.99 _cEUR _d94.90
490			_aGraduate texts in mathematics, _v287
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 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			_aBohr-Caratheodory theorem
650			_aCauchy-Riemann equation
650			_aEuler reflection formula
650			_aHardy-Ramanujan partition function theorem
650			_aKaramata tauberian theorem
650			_aLalesco problem
650			_aMapping theorem
650			_aPaley-Fischer theorem
650			_aTauberian theorem
650			_aUniformization theorem
650			_aBorel-Carathesdory theorem
650			_aRiesz-Fischer theorem
700			_aWong, Roderick S. C.
942			_2ddc _cBK