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Advance Real Analysis (Digital Second Edition) by Anthony W. Knapp


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Advance Real Analysis (Digital Second Edition) written by Anthony W. Knapp . This is an other book of mathematics cover the following topics.

  • INTRODUCTION TO BOUNDARY-VALUE PROBLEMS
    Partial Differential Operators, Separation of Variables, Sturm–Liouville Theory, Problems

  • COMPACT SELF-ADJOINT OPERATORS
    Compact Operators, Spectral Theorem for Compact Self-Adjoint Operators, Hilbert–Schmidt Theorem, Unitary Operators, Classes of Compact Operators, Problems

  • TOPICS IN EUCLIDEAN FOURIER ANALYSIS
    Tempered Distributions, Weak Derivatives and Sobolev Spaces, Harmonic Functions, Hp Theory, Calderon–Zygmund ´ Theorem, Applications of the Calderon–Zygmund ´ Theorem, Multiple Fourier Series, Application to Traces of Integral Operators, Problems

  • TOPICS IN FUNCTIONAL ANALYSIS
    Topological Vector Spaces, C∞(U), Distributions, and Support, Weak and Weak-Star Topologies, Alaoglu’s Theorem, Stone Representation Theorem, Linear Functionals and Convex Sets, Locally Convex Spaces, Topology on C∞ com(U), Krein–Milman Theorem, Fixed-Point Theorems, Gelfand Transform for Commutative C∗ Algebras, Spectral Theorem for Bounded Self-Adjoint Operators, Problems

  • DISTRIBUTIONS
    Continuity on Spaces of Smooth Functions, Elementary Operations on Distributions, Convolution of Distributions, Role of Fourier Transform, Fundamental Solution of Laplacian, Problems

  • COMPACT AND LOCALLY COMPACT GROUPS
    Topological Groups, Existence and Uniqueness of Haar Measure, Modular Function, Invariant Measures on Quotient Spaces, Convolution and L p Spaces, Representations of Compact Groups, Peter–Weyl Theorem, Fourier Analysis Using Compact Groups, Problems

  • ASPECTS OF PARTIAL DIFFERENTIAL EQUATIONS
    Introduction via Cauchy Data, Orientation, Local Solvability in the Constant-Coefficient Case, Maximum Principle in the Elliptic Second-Order Case, Parametrices for Elliptic Equations with Constant Coefficients, Method of Pseudodifferential Operators, Problems

  • ANALYSIS ON MANIFOLDS
    Differential Calculus on Smooth Manifolds, Vector Fields and Integral Curves, Identification Spaces, Vector Bundles, Distributions and Differential Operators on Manifolds, More about Euclidean Pseudodifferential Operators, Pseudodifferential Operators on Manifolds, Further Developments, Problems

  • FOUNDATIONS OF PROBABILITY
    Measure-Theoretic Foundations, Independent Random Variables, Kolmogorov Extension Theorem, Strong Law of Large Numbers, Convergence in Distribution, Portmanteau Lemma, Characteristic Functions, Levy ´ Continuity Theorem, Central Limit Theorem, Statistical Inference and Gosset’s t Distribution, Problems

  • INTRODUCTION TO WAVELETS
    Introduction, Haar Wavelet, Multiresolution Analysis, Shannon Wavelet, Construction of a Wavelet from a Scaling Function, Meyer Wavelets, Splines, Battle–Lemarie´ Wavelets, Daubechies Wavelets, Smoothness Questions, A Quick Introduction to Applications, Problems

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