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Haar Series and Linear Operators

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...

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Bibliographic Details
Main Authors: Novikov, I., Semenov, E. (Author)
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 1997, 1997
Edition:1st ed. 1997
Series:Mathematics and Its Applications
Subjects:
Functional Analysis
Functions Of Real Variables
Fourier Analysis
Approximations And Expansions
Operator Theory
Real Functions
Approximation Theory
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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. Subsequences of the Haar System
  • 16. Criterion of Equivalence of the Haar and Franklin Systems in R.I. Spaces
  • 17. Olevskii Systems
  • References

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