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035   $a(DE-B1597)9781400881536
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101 0 $aeng
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200 10$aRandom Fourier Series with Applications to Harmonic Analysis. (AM-101), Volume 101 /$fGilles Pisier, Michael B. Marcus
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$dİ1982
215   $a1 online resource (161 pages)
225 0 $aAnnals of Mathematics Studies ;$v241
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a0-691-08289-8 
311   $a0-691-08292-8 
320   $aIncludes bibliographical references and index.
327   $tFrontmatter -- $tCONTENTS -- $tCHAPTER I: INTRODUCTION -- $tCHAPTER II: PRELIMINARIES -- $tCHAPTER III: RANDOM FOURIER SERIES ON LOCALLY COMPACT ABELIAN GROUPS -- $tCHAPTER IV: THE CENTRAL LIMIT THEOREM AND RELATED QUESTIONS -- $tCHAPTER V: RANDOM FOURIER SERIES ON COMPACT NON-ABELIAN GROUPS -- $tCHAPTER VI: APPLICATIONS TO HARMONIC ANALYSIS -- $tCHAPTER VII: ADDITIONAL RESULTS AND COMMENTS -- $tREFERENCES -- $tINDEX OF TERMINOLOGY -- $tINDEX OF NOTATIONS -- $tBackmatter
330   $aIn this book the authors give the first necessary and sufficient conditions for the uniform convergence a.s. of random Fourier series on locally compact Abelian groups and on compact non-Abelian groups. They also obtain many related results. For example, whenever a random Fourier series converges uniformly a.s. it also satisfies the central limit theorem. The methods developed are used to study some questions in harmonic analysis that are not intrinsically random. For example, a new characterization of Sidon sets is derived.The major results depend heavily on the Dudley-Fernique necessary and sufficient condition for the continuity of stationary Gaussian processes and on recent work on sums of independent Banach space valued random variables. It is noteworthy that the proofs for the Abelian case immediately extend to the non-Abelian case once the proper definition of random Fourier series is made. In doing this the authors obtain new results on sums of independent random matrices with elements in a Banach space. The final chapter of the book suggests several directions for further research.
410  0$aAnnals of mathematics studies ;$vNumber 101.
606   $aFourier series
606   $aHarmonic analysis
610   $aAbelian group.
610   $aAlmost periodic function.
610   $aAlmost surely.
610   $aBanach space.
610   $aBig O notation.
610   $aCardinality.
610   $aCentral limit theorem.
610   $aCircle group.
610   $aCoefficient.
610   $aCommutative property.
610   $aCompact group.
610   $aCompact space.
610   $aComplex number.
610   $aContinuous function.
610   $aCorollary.
610   $aDiscrete group.
610   $aEquivalence class.
610   $aExistential quantification.
610   $aFinite group.
610   $aFourier series.
610   $aGaussian process.
610   $aHaar measure.
610   $aHarmonic analysis.
610   $aIndependence (probability theory).
610   $aInequality (mathematics).
610   $aInteger.
610   $aIrreducible representation.
610   $aNon-abelian group.
610   $aNon-abelian.
610   $aNormal distribution.
610   $aOrthogonal group.
610   $aOrthogonal matrix.
610   $aProbability distribution.
610   $aProbability measure.
610   $aProbability space.
610   $aProbability.
610   $aRandom function.
610   $aRandom matrix.
610   $aRandom variable.
610   $aRate of convergence.
610   $aReal number.
610   $aRing (mathematics).
610   $aScientific notation.
610   $aSet (mathematics).
610   $aSlepian's lemma.
610   $aSmall number.
610   $aSmoothness.
610   $aStationary process.
610   $aSubgroup.
610   $aSubset.
610   $aSummation.
610   $aTheorem.
610   $aUniform convergence.
610   $aUnitary matrix.
610   $aVariance.
615  0$aFourier series.
615  0$aHarmonic analysis.
676   $a515/.2433
700   $aMarcus$b Michael B., $049046
702   $aPisier$b Gilles, 
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154747303321
996   $aRandom Fourier Series with Applications to Harmonic Analysis. (AM-101), Volume 101$92785798
997   $aUNINA