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  • © 1997

Haar Series and Linear Operators

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

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xv
  2. Preliminaries

    • Igor Novikov, Evgenij Semenov
    Pages 1-13
  3. Definition and Main Properties of the Haar System

    • Igor Novikov, Evgenij Semenov
    Pages 15-18
  4. Convergence of Haar Series

    • Igor Novikov, Evgenij Semenov
    Pages 19-24
  5. Basis Properties of the Haar System

    • Igor Novikov, Evgenij Semenov
    Pages 25-31
  6. The Unconditionality of the Haar system

    • Igor Novikov, Evgenij Semenov
    Pages 33-39
  7. The Paley Function

    • Igor Novikov, Evgenij Semenov
    Pages 41-50
  8. Fourier-Haar Coefficients

    • Igor Novikov, Evgenij Semenov
    Pages 51-72
  9. The Haar system and martingales

    • Igor Novikov, Evgenij Semenov
    Pages 73-82
  10. Reproducibility of the Haar system

    • Igor Novikov, Evgenij Semenov
    Pages 83-87
  11. Generalized Haar Systems and Monotone Bases

    • Igor Novikov, Evgenij Semenov
    Pages 89-107
  12. Haar System Rearrangements

    • Igor Novikov, Evgenij Semenov
    Pages 109-125
  13. Fourier-Haar Multipliers

    • Igor Novikov, Evgenij Semenov
    Pages 127-131
  14. Pointwise Estimates of Multipliers

    • Igor Novikov, Evgenij Semenov
    Pages 133-142
  15. Estimates of Multipliers in L 1

    • Igor Novikov, Evgenij Semenov
    Pages 143-149
  16. Subsequences of the Haar system

    • Igor Novikov, Evgenij Semenov
    Pages 151-167
  17. Olevskii System

    • Igor Novikov, Evgenij Semenov
    Pages 191-193
  18. Back Matter

    Pages 195-224

About this book

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.

Reviews

` ... this book will prove useful to the specialist. The reviewer is happy to put it on his shelf along with the other references in dyadic harmonic analysis. He plans to use it when the need arises.'
Mathematical Reviews, 98h

Authors and Affiliations

  • Department of Mathematics, Voronezh State University, Voronezh, Russia

    Igor Novikov, Evgenij Semenov

Bibliographic Information

Buy it now

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access