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Haar Series and Linear Operators

  • Igor Novikov
  • Evgenij Semenov

Part of the Mathematics and Its Applications book series (MAIA, volume 367)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Igor Novikov, Evgenij Semenov
    Pages 1-13
  3. Igor Novikov, Evgenij Semenov
    Pages 15-18
  4. Igor Novikov, Evgenij Semenov
    Pages 19-24
  5. Igor Novikov, Evgenij Semenov
    Pages 25-31
  6. Igor Novikov, Evgenij Semenov
    Pages 33-39
  7. Igor Novikov, Evgenij Semenov
    Pages 41-50
  8. Igor Novikov, Evgenij Semenov
    Pages 51-72
  9. Igor Novikov, Evgenij Semenov
    Pages 73-82
  10. Igor Novikov, Evgenij Semenov
    Pages 83-87
  11. Igor Novikov, Evgenij Semenov
    Pages 89-107
  12. Igor Novikov, Evgenij Semenov
    Pages 109-125
  13. Igor Novikov, Evgenij Semenov
    Pages 127-131
  14. Igor Novikov, Evgenij Semenov
    Pages 133-142
  15. Igor Novikov, Evgenij Semenov
    Pages 143-149
  16. Igor Novikov, Evgenij Semenov
    Pages 151-167
  17. Igor Novikov, Evgenij Semenov
    Pages 191-193
  18. Back Matter
    Pages 195-224

About this book

Introduction

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.

Keywords

DEX Equivalence Martingale Monotone Volume boundary element method continuous function convergence form function functional functional analysis operator operator theory system

Authors and affiliations

  • Igor Novikov
    • 1
  • Evgenij Semenov
    • 1
  1. 1.Department of MathematicsVoronezh State UniversityVoronezhRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-1726-7
  • Copyright Information Springer Science+Business Media B.V. 1997
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4693-2
  • Online ISBN 978-94-017-1726-7
  • Buy this book on publisher's site
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