Fourier series with respect to general orthogonal systems

Author(s)

Bibliographic Information

Fourier series with respect to general orthogonal systems

A.M. Olevskiĭ ; translated from the Russian by B.P. Marshall and H.J. Christoffers

（Ergebnisse der Mathematik und ihrer Grenzgebiete, Bd. 86）

Springer-Verlag, 1975

  • : us
  • : gw

Other Title

Ri︠a︡dy Furʹe po obshchim ortogonalʹnym sistemam

Uniform Title

Ri︠a︡dy Furʹe po obshchim ortogonalʹnym sistemam

Available at  / 65 libraries

Search this Book/Journal

Note

Translation of Ri︠a︡dy Furʹe po obshchim ortogonalʹnym sistemam

Bibliography: p. [128]-134

Includes index

Description and Table of Contents

Description

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 {<!-- -->

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.

by "Nielsen BookData"

Related Books： 1-1 of 1

Details

Page Top