000			a
999			_c31917 _d31917
008			230420b xxu||||| |||| 00| 0 eng d
020			_a9780367237677
082			_a515.98 _bKYT
100			_aKythe, Prem K
245			_aComplex analysis : conformal inequalities and the Bieberbach conjecture
260			_bCRC Press, _c2016 _aBoca Raton :
300			_axx, 343 p. ; _bill. _c23 cm
365			_b1995.00 _cINR _d01
490			_aMonographs and Research Notes in Mathematics
504			_aIncludes bibliographical references and index.
520			_aComplex Analysis: Conformal Inequalities and the Bieberbach Conjecture discusses the mathematical analysis created around the Bieberbach conjecture, which is responsible for the development of many beautiful aspects of complex analysis, especially in the geometric-function theory of univalent functions. Assuming basic knowledge of complex analysis and differential equations, the book is suitable for graduate students engaged in analytical research on the topics and researchers working on related areas of complex analysis in one or more complex variables. The author first reviews the theory of analytic functions, univalent functions, and conformal mapping before covering various theorems related to the area principle and discussing Löwner theory. He then presents Schiffer’s variation method, the bounds for the fourth and higher-order coefficients, various subclasses of univalent functions, generalized convexity and the class of α-convex functions, and numerical estimates of the coefficient problem. The book goes on to summarize orthogonal polynomials, explore the de Branges theorem, and address current and emerging developments since the de Branges theorem.
650			_aFunctional analysis
650			_aCalculus
650			_aAskey-Gasper theorem
650			_aBazilevich functions
650			_aCauchy's argument principle
650			_aDirichlet integral
650			_aFitzgerald inequalirty
650			_a Green's formulas
650			_a Harnack's theorem
650			_aKoebe function
650			_aLebedev-Milin area theorem
650			_aMilin's conjecture
650			_aRiemann mapping theorem
650			_aSchwarz function
650			_aWeirstrans theorem
942			_2ddc _cBK