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Fourier series with respect to general orthogonal systems

Author: A M Olevskiĭ
Publisher: Berlin ; New York : Springer-Verlag, 1975.
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete, Bd. 86.
Edition/Format:   Print book : EnglishView all editions and formats
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Additional Physical Format: Online version:
Olevskiĭ, A.M., 1939-
Fourier series with respect to general orthogonal systems.
Berlin ; New York : Springer-Verlag, 1975
(OCoLC)762219831
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: A M Olevskiĭ
ISBN: 0387071032 9780387071039 3540071032 9783540071037
OCLC Number: 1195129
Notes: Translation of Ri︠a︡dy Furʹe po obshchim ortogonalʹnym sistemam.
Description: viii, 136 pages ; 25 cm.
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.
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete, Bd. 86.
Other Titles: Ri︠a︡dy Furʹe po obshchim ortogonalʹnym sistemam.
Responsibility: A.M. Olevskiĭ ; translated from the Russian by B.P. Marshall and H.J. Christoffers.

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