## Haar Series and Linear OperatorsIn 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. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Definition and Main Properties of the Haar System | 15 |

The Unconditionally of the Haar System | 33 |

FourierHaar Coefficients | 51 |

Copyright | |

9 other sections not shown

### Other editions - View all

### Common terms and phrases

1)-splitting of degree a-algebra Banach space basis of lp block basis bounded in Lp boundedness Chapter characteristic function condition conditional expectation consider the function construct contractive projection converges Corollary defined Definition Denote disjoint disjoint sets dyadic intervals dyadic tree estimate exists a constant fc=i fc=l finite Fourier-Haar coefficients Fourier-Haar series Franklin system function g function on 0,1 Haar functions Haar series Haar system Hence Holder inequality induction integer interpolation theorem ISBN isometric isomorphic last inequality Lemma Let us prove linear operator linear span Marcinkiewicz interpolation theorem martingale martingale-difference sequence measure mes{t monotone basis n,fc)en non-increasing non-negative Nonlinear norm Olevskii oo oo Orlicz spaces polynomials proof of Theorem PyN(t Rademacher functions rearrangement Remark Russian satisfies Section 1.d separable r.i. space sequence of scalars smooth separable r.i. subsequence subsets subspace unconditional basis unit vector basis valid xn(t