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Real and Complex Analysis By Walter Rudin

MathSchoolinternational.com contain houndreds of Free Math e-Books. Which cover almost all topics of mathematics. To see an extisive list of Complex Analysis eBooks . We hope mathematician or person who’s interested in mathematics like these books.


Real and Complex Analysis (third edition) by Walter Rudin . This is an other great free downloadable mathematics book cover the following topics of complex number.

  • Abstract Integration
    Set-theoretic notations and terminology, The concept of measurability, Simple functions, Elementary properties of measures, Arithmetic in [0, 00], Integration of positive functions, Integration of complex functions, The role played by sets of measure zero, Exercises

  • Positive Borel Measures
    Vector spaces, Topological preliminaries, The Riesz representation theorem, Regularity properties of Borel measures, Lebesgue measure, Continuity properties of measurable functions, Exercises

  • LP-Spaces
    Convex functions and inequalities, The LP-spaces, Approximation by continuous functions, Exercises

  • Elementary Hilbert Space Theory
    Inner products and linear functionals, Orthonormal sets, Trigonometric series, Exercises

  • Examples of Banach Space Techniques
    Banach spaces, Consequences of Baire's theorem, Fourier series of continuous functions, Fourier coefficients of LI-functions, The Hahn-Bana.eh theorem, An abstract approach to the Poisson integral, Exercises

  • Complex Measures
    Total variation, Absolute continuity, Consequences of the Radon-Nikodym theorem, Bounded linear functionals on LP, The Riesz representation theorem, Exercises

  • Differentiation
    Derivatives of measures, The fundamental theorem of Calculus, Differentiable transformations, Exercises

  • Integration on Product Spaces
    Measurability on cartesian products, Product measures, The Fubini theorem, Completion of product measures, Convolutions, Distribution functions, Exercises

  • Fourier Transforms
    Formal properties, The inversion theorem, The Plancherel theorem, The Banach algebra LI, Exercises

  • Elementary Properties of Holomorphic
    Functions, Complex differentiation, Integration over paths, The local Cauchy theorem, The power series representation, The open mapping theorem, The global Cauchy theorem, The calculus of residues, Exercises

  • Harmonic Functions
    The Cauchy-Riemann equations, The Poisson integral, The mean value property, Boundary behavior of Poisson integrals, Representation theorems, Exercises

  • The Maximum Modulus Principle
    Introduction, The Schwarz lemma, The Phragmen-LindelOf method, An interpolation theorem, A converse of the maximum modulus theorem, Exercises

  • Approximation by Rational Functions
    Preparation, Runge's theotem, The Mittag-Lerner theorem, Simply connected regions, Exercises

  • Conformal Mapping
    Preservation of angles, Linear fractional transformations, Normal families, The Riemann mapping theorem, The class [I', Continuity at the boundary, Conformal mapping of an annulus, Exercises

  • Zeros of Holomorphic Functions
    Infinite products, The Weierstrass factorization theorem, An interpolation problem, Jensen's formula, Blaschke products, The Miintz-Szasz theorem, Exercises

  • Analytic Continuation
    Regular points and singular points, Continuation along curves, The monodron;Iy theorem, Construction of a modular function, The Picard theorem, Exercises

  • HP-Spaces
    Subharmonic functions, The spaces HP and N, The theorem of F. and M. Riesz, Factorization "theorems, The shift operator, Conjugate functions, Exercises

  • Elementary Theory of Banach Algebras
    Introduction, The invertible elements, Ideals and homomorphisms, Applications, Exercises

  • Holomorphic Fourier Transforms
    Introduction, Two theorems of Paley and Wiener, Quasi-analytic classes, The Denjoy-Carleman theorem, Exercises

  • Uniform Approximation by Polynomials
  • Introduction, Some lemmas, Mergelyan's theorem, Exercises, Appendix: Hausdorff's Maximality Theorem, Notes and Comments, Bibliography, List of Special Symbols, Index

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    Math Books of COMPLEX ANALYSIS

    Geometry of Complex Numbers by Hans Schwerdtfeger
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  • English
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