Overview

The fundamental problem of the theory of Fourier series consists of the investigation of the connections between the metric properties of the function expanded, the behavior of its Fourier coefficients {cn} with respect to an ortho­ normal system of functions {

Full Product Details

Author:   A. Olevskii ,  B.P. Marshall ,  H.J. Christoffers
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of the original 1st ed. 1975
Volume:   86
Dimensions:   Width: 17.00cm , Height: 0.80cm , Length: 24.40cm
Weight:   0.276kg
ISBN:  

9783642660580

ISBN 10:   3642660584
Pages:   138
Publication Date:   15 November 2011
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Terminology. Preliminary Information.- I. Convergence of Fourier Series in the Classical Sense. Lebesgue Functions of Bounded Systems.- § 1. The Fundamental Inequality.- § 2. The Logarithmic Growth of the Lebesgue Functions. Divergence of Fourier Series.- § 3. Series with Decreasing Coefficients.- § 4. Generalizations, Counterexamples, Problems.- § 5. The Stability of the Orthogonalization Operator.- II. Convergence Almost Everywhere; Conditions on the Coefficients.- §1. The Class S?.- § 2. Garsia’s Theorem.- § 3. The Coefficients of Convergent Series in Complete Systems.- § 4. Extension of a System of Functions to an ONS.- III. Properties of Complete Systems; the Role of the Haar System.- § 1. The Basic Construction.- § 2. Divergent Fourier Series.- § 3. Bases in Function Spaces and Majorants of Fourier Series.- § 4. Fourier Coefficients of Continuous Functions.- § 5. Some More Results about the Haar System.- IV. Series from L2 and Peculiarities of Fourier Series from the Spaces Lp.- §1. The Matrices Ak.- § 2. Lebesgue Functions and Convergence Almost Everywhere.- § 3. Convergence of Fourier Series of Functions from Various Classes.- §4. Sums of Fourier Series.- § 5. Conditional Bases in Hubert Space.

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