A Comprehensive Course in Analysis

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· 제목 : A Comprehensive Course in Analysis (Hardcover)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 일반
· ISBN : 9781470410988
· 쪽수 : 3259쪽
· 출판일 : 2015-12-21

Contents for Part 1 (Real Analysis): Preliminaries
Topological spaces
A first look at Hilbert spaces and Fourier series
Measure theory
Convexity and Banach spaces
Tempered distributions and the Fourier transform
Bonus chapter: Probability basics
Bonus chapter: Hausdorff measure and dimension
Bonus chapter: Inductive limits and ordinary distributions
Bibliography
Symbol index
Subject index
Author index
Index of capsule biographies
Contents for Part 2A (Basic Complex Analysis): Preliminaries
The Cauchy integral theorem: Basics Consequences of the Cauchy integral formula
Chains and the ultimate Cauchy integral theorem
More consequences of the CIT
Spaces of analytic functions
Fractional linear transformations
Conformal maps
Zeros of analytic functions and product formulae
Elliptic functions
Selected additional topics
Bibliography
Symbol index
Subject index
Author index
Index of capsule biographies
Contents for Part 2B (Advanced Complex Analysis): Riemannian metrics and complex analysis
Some topics in analytic number theory
Ordinary differential equations in the complex domain
Asymptotic methods
Univalent functions and Loewner evolution
Nevanlinna theory
Bibliography
Symbol index
Subject index
Author index
Index of capsule biographies
Contents for Part 3 (Harmonic Analysis): Preliminaries
Pointwise convergence almost everywhere
Harmonic and subharmonic functions
Bonus chapter: Phase space analysis $H^p$ spaces and boundary values of analytic functions on the unit disk
Bonus chapter: More inequalities
Bibliography
Symbol index
Subject index
Author index
Index of capsule biographies
Contents for Part 4 (Operator Theory): Preliminaries
Operator basics
Compact operators, mainly on a Hilbert space
Orthogonal polynomials
The spectral theorem
Banach algebras
Bonus chapter: Unbounded self-adjoint operators
Bibliography
Symbol index
Subject index
Author index
Index of capsule biographies