Synopses & Reviews
This classic text features a sophisticated treatment of Fourier's pioneering method for expressing periodic functions as an infinite series of trigonometrical functions. Geared toward mathematicians already familiar with the elements of Lebesgue's theory of integration, the text serves as an introduction to Zygmund's standard treatise.
Beginning with a brief introduction to some generalities of trigonometrical series, the book explores the Fourier series in Hilbert space as well as their convergence and summability. The authors provide an in-depth look at the applications of previously outlined theorems and conclude with an examination of general trigonometrical series. Ideally suited for both individual and classroom study, this incisive text offers advanced undergraduate and graduate students in mathematics, physics, and engineering a valuable tool in understanding the essentials of the Fourier series.
Synopsis
Geared toward mathematicians already familiar with the elements of Lebesgue's theory of integration, this classic graduate-level text begins with a brief introduction to some generalities of trigonometrical series. Discussions of the Fourier series in Hilbert space lead to an examination of further properties of trigonometrical Fourier series and related subjects. 1956 edition.
Synopsis
Classic graduate-level text discusses the Fourier series in Hilbert space, examines further properties of trigonometrical Fourier series, and concludes with a detailed look at the applications of previously outlined theorems. 1956 edition.
Synopsis
Geared toward mathematicians already familiar with the elements of Lebesgue's theory of integration, this classic, graduate-level text begins with a brief introduction to some generalities about trigonometrical series. Discussions of the Fourier series in Hilbert space lead to an examination of further properties of trigonometrical Fourier series, more. 1956 edition.
Table of Contents
Preface; Notations
I. Generalities
II. Fourier series in Hilbert space
III. Further properties of trigonometrical Fourier series
IV. Convergence of Fourier series
V. Summability of Fourier series
VI. Applications of the theorems of Chapter V
VII. General trigonometrical series
Notes