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About this book :-
Advance Real Analysis (2E) written by Anthony W. Knapp
This book and its companion volume Basic Real Analysis systematically develop concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. The two books together contain what the young mathematician needs to know about real analysis in order to communicate well with colleagues in all branches of mathematics.
The books are written as textbooks, and their primary audience is students who are learning the material for the first time and who are planning a career in which they will use advanced mathematics professionally. Much of the material in the books corresponds to normal course work. Nevertheless, it is often the case that core mathematics curricula, time-limited as they are, do not include all the topics that one might like. Thus the book includes important topics that are sometimes skipped in required courses but that the professional mathematician will ultimately want to learn by self-study.
Book Detail :-
Title: Advance Real Analysis
Author(s): Anthony W. Knapp
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About Author :-
Author Anthony W. Knapp (born 1941, New Jersey) is an American mathematician at the State University of New York, Stony Brook working on representation theory, who classified the tempered representations of a semisimple Lie group. He won the Leroy P. Steele Prize for Mathematical Exposition in 1997. He became a fellow of the American Mathematical Society in 2012.
All Famous Books of this Author :-
Here is list all books, text books, editions, versions or solution manuals avaliable of this author, We recomended you to download all.
• Download PDF Basic Real Analysis by Anthony Knapp
• Download PDF Advance Real Analysis (Digital Second Edition) by Anthony Knapp
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Book Contents :-
Advance Real Analysis (2E) written by Anthony W. Knapp 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
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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