Fourier Series with Respect to General Orthogonal Systems
(Sprache: Englisch)
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 {
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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 {
Inhaltsverzeichnis zu „Fourier Series with Respect to General Orthogonal Systems “
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.
Bibliographische Angaben
- Autor: A. Olevskii
- 2011, 138 Seiten, Maße: 24,4 cm, Kartoniert (TB), Englisch
- Übersetzung: Marshall, B.P.; Christoffers, H.J.
- Verlag: Springer
- ISBN-10: 3642660584
- ISBN-13: 9783642660580
Sprache:
Englisch
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