Analysis II Differential and Integral Calculus, Fourier Series, Holomorphic Functions

Analysis II Differential and Integral Calculus, Fourier Series, Holomorphic Functions / by Roger Godement.

Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonl...

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Bibliographic Details
Main Author: Godement, Roger (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2005.
Edition:1st ed. 2005.
Series:Universitext,
Springer eBook Collection.
Subjects:
Functions of real variables.
Measure theory.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • Differential and Integral Calculus
  • The Riemann Integral
  • Integrability Conditions
  • The “Fundamental Theorem” (FT)
  • Integration by parts
  • Taylor’s Formula
  • The change of variable formula
  • Generalised Riemann integrals
  • Approximation Theorems
  • Radon measures in ? or ?
  • Schwartz distributions
  • Asymptotic Analysis
  • Truncated expansions
  • Summation formulae
  • Harmonic Analysis and Holomorphic Functions
  • Analysis on the unit circle
  • Elementary theorems on Fourier series
  • Dirichlet’s method
  • Analytic and holomorphic functions
  • Harmonic functions and Fourier series
  • From Fourier series to integrals.

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