Real and Complex AnalysisMcGraw-Hill Education, 1987 - 416 pages This is an advanced text for the one- or two-semester course in analysis taught primarily to math, science, computer science, and electrical engineering majors at the junior, senior or graduate level. The basic techniques and theorems of analysis are presented in such a way that the intimate connections between its various branches are strongly emphasized. The traditionally separate subjects of 'real analysis' and 'complex analysis' are thus united in one volume. Some of the basic ideas from functional analysis are also included. This is the only book to take this unique approach. The third edition includes a new chapter on differentiation. Proofs of theorems presented in the book are concise and complete and many challenging exercises appear at the end of each chapter. The book is arranged so that each chapter builds upon the other, giving students a gradual understanding of the subject. This text is part of the Walter Rudin Student Series in Advanced Mathematics. |
Table des matières
Abstract Integration | 5 |
Positive Borel Measures | 33 |
LPSpaces | 61 |
Droits d'auteur | |
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Expressions et termes fréquents
A₁ assume B₁ Banach algebra Banach space Blaschke product Borel measure boundary bounded linear functional Cauchy Chap closed path compact set compact subset complex function complex numbers conformal mapping constant contains continuous function converges uniformly convex countable D₁ defined Definition dense differentiable disjoint entire function Exercise exists finite follows formula Fourier transform function f half plane harmonic function Hence Hilbert space holds holomorphic functions implies inequality Lebesgue measure Lemma linear fractional transformation mapping Math maximal norm Note one-to-one open set Poisson integral polynomials PROOF Let proof of Theorem properties Prove that ƒ r₂ radius real axis real number region S-invariant satisfies sequence shows simply connected subspace Suppose ƒ supremum Theorem Suppose u₁ vector space zero