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Mathematics and Its Applications #367: Haar Series and Linear Operators

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Mathematics and Its Applications #367: Haar Series and Linear Operators Cover

 

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Publisher Comments:

In 1909 Alfred Haar introduced into analysis a remarkable system which bears his name. The Haar system is a complete orthonormal system on [0,1] and the Fourier-Haar series for arbitrary continuous function converges uniformly to this function. This volume is devoted to the investigation of the Haar system from the operator theory point of view. The main subjects treated are: classical results on unconditional convergence of the Haar series in modern presentation; Fourier-Haar coefficients; reproducibility; martingales; monotone bases in rearrangement invariant spaces; rearrangements and multipliers with respect to the Haar system; subspaces generated by subsequences of the Haar system; the criterion of equivalence of the Haar and Franklin systems. Audience: This book will be of interest to graduate students and researchers whose work involves functional analysis and operator theory.

Table of Contents

1. Preliminaries. 2. Definition and Main Properties of the Haar System. 3. Convergence of Haar Series. 4. Basis Properties of the Haar System. 5. The Unconditionality of the Haar System. 6. The Paley Function. 7. Fourier-Haar Coefficients. 8. The Haar System and Martingales. 9. Reproducibility of the Haar System. 10. Generalized Haar Systems and Monotone Bases. 11. Haar System Rearrangements. 12. Fourier-Haar Multipliers. 13. Pointwise Estimates of Multipliers. 14. Estimates of Multipliers in L1. 15. Subsequence of the Haar System. 16. Criterion of Equivalence of the Haar and Franklin Systems in R.I. Spaces. 17. Olevskii System. References. Index.

Product Details

ISBN:
9789048146932
Author:
Novikov, I.
Publisher:
Springer
Author:
Semenov, E.
Location:
Dordrecht
Subject:
Functional Analysis
Subject:
Real functions
Subject:
Approximations and Expansions
Subject:
Fourier analysis
Subject:
Operator theory
Subject:
Mathematics : Functional Analysis
Subject:
Mathematical Analysis
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Copyright:
Edition Description:
Softcover reprint of hardcover 1st ed. 1996
Series:
Mathematics and Its Applications (closed)
Series Volume:
367
Publication Date:
20101207
Binding:
TRADE PAPER
Language:
English
Pages:
236
Dimensions:
240 x 160 mm 374 gr

Related Subjects

Science and Mathematics » Chemistry » Physical Chemistry
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Functional Analysis

Mathematics and Its Applications #367: Haar Series and Linear Operators New Trade Paper
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