Description

Book Synopsis


Table of Contents
  • 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

A Comprehensive Course in Analysis 5 Volume Set

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    £298.80

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    RRP £332.00 – you save £33.20 (10%)

    Order before 4pm tomorrow for delivery by Mon 22 Jun 2026.

    A Hardback by Barry Simon

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      View other formats and editions of A Comprehensive Course in Analysis 5 Volume Set by Barry Simon

      Publisher: MP-AMM American Mathematical
      Publication Date: 12/30/2015 12:00:00 AM
      ISBN13: 9781470410988, 978-1470410988
      ISBN10: 1470410982

      Description

      Book Synopsis


      Table of Contents
      • 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

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