1] and the Fourier-Haar series for arbitrarycontinuous function converges uniformly to this function. .This volume is devoted to the investigation of the Haar system fromthe operator theory point of view. The main subjects treated are:classical results on unconditional convergence of the Haar series
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Fourier-Haar Multipliers,FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8% qacaaIXaGaeyipaWJaamiCaiabgYda8iabg6HiLkaacYcadaWcaaWd% aeaapeGaaGymaaWdaeaapeGaamiCaaaacqGHRaWkpaGaafiiamaala% aabaGaaGymaaqaaiaadchadaahaaWcbeqaaiaaigdaaaaaaOGaeyyp% a0JaaGymaaaa!4432!$$1 < p < infty ,frac{1}{p} + { ext{ }}frac{1}{{{p^1}}} = 1$$, then
Frédérique Cerisier,Fabien Postel-VinaycqGH9aqpcaGG7bGaeqyTdu2a% aSbaaSqaaiaad2gaaeqaaOGaaiyFamaaDaaaleaacaWGTbGaeyypa0% JaaGymaaqaaiabg6HiLcaakiaacYcacaaMe8UaeqyTdu2aaSbaaSqa% aiaad2gaaeqaaOGaeyypa0JaeyySaeRaaGymaiaac6caaaa!5464!]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$varepsilon = { {varepsilon _m}} _{m = 1}^infty ,;{varepsilon _m} = pm 1.$$
The Unconditionality of the Haar system,cqGH9aqpcaGG7bGaeqyTdu2a% aSbaaSqaaiaad2gaaeqaaOGaaiyFamaaDaaaleaacaWGTbGaeyypa0% JaaGymaaqaaiabg6HiLcaakiaacYcacaaMe8UaeqyTdu2aaSbaaSqa% aiaad2gaaeqaaOGaeyypa0JaeyySaeRaaGymaiaac6caaaa!5464!]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$varepsilon = { {varepsilon _m}} _{m = 1}^infty ,;{varepsilon _m} = pm 1.$$
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ltipliers with respect to theHaar 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 andresearchers whose work involves functional analysis and operatortheory.978-90-481-4693-2978-94-017-1726-7
Reproducibility of the Haar system,situations that the subsequence {x.}. is reproduced as a block basis of {y.}.. Of particular interest is the case when the above mentioned assertion is valid for the basis {x.}. itself. To investigate such situations the following definition is introduced in .
Criterion of Equivalence of the Haar and Franklin Systems in R.I. Spaces, fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqaaeaada% GacaqaaiaadIgacaWGTbaacaGL9baaaiaawUhaamaaDaaaleaacaaI% WaaabaGaeyOhIukaaaaa!3C63!]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$left{ {left. {hm}
ight}}
ight._0^infty$$ Recall that