A comprehensive course in analysis

A comprehensive course in analysis: Basic complex analysis

by Simon, Barry

Type Book
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A Comprehensive Course in Analysis by Poincar Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis

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Title Statements

  • Full title :A comprehensive course in analysis. : Basic complex analysis / Barry Simon

Summary

A Comprehensive Course in Analysis by Poincar Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis

Read More ↓

Edition Statements

  • Publication Date:2015

Publication Statements

Notes

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 $Hp̂$ 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

The Physical Object

  • Description:6 bd

Edition Identifiers

  • ISBN:9781470410988, 1470410982, 9781470410995, 1470410990, 9781470411008, 1470411008, 9781470411015, 1470411016, 9781470411022, 1470411024, 9781470411039, 1470411032
  • oclc:ocn944232978
  • LC Classification:QA300
  • Dewey Decimal:515

Subjects

Brownian motion processes Complex analysis Harmonic analysis Mathematical analysis Mathematical analysis -- Textbooks mathematics Operator theory Picard's theorem Real analysis Textbooks

Writers

Simon, Barry

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