## Random Fourier Series with Applications to Harmonic AnalysisThe changes to U.S. immigration law that were instituted in 1965 have led to an influx of West African immigrants to New York, creating an enclave Harlem residents now call ''Little Africa.'' These immigrants are immediately recognizable as African in their wide-sleeved robes and tasseled hats, but most native-born members of the community are unaware of the crucial role Islam plays in immigrants' lives. Zain Abdullah takes us inside the lives of these new immigrants and shows how they deal with being a double minority in a country where both blacks and Muslims are stigmatized. Dealing with this dual identity, Abdullah discovers, is extraordinarily complex. Some longtime residents embrace these immigrants and see their arrival as an opportunity to reclaim their African heritage, while others see the immigrants as scornful invaders. In turn, African immigrants often take a particularly harsh view of their new neighbors, buying into the worst stereotypes about American-born blacks being lazy and incorrigible. And while there has long been a large Muslim presence in Harlem, and residents often see Islam as a force for social good, African-born Muslims see their Islamic identity disregarded by most of their neighbors. Abdullah weaves together the stories of these African Muslims to paint a fascinating portrait of a community's efforts to carve out space for itself in a new country. -- Book jacket. |

### What people are saying - Write a review

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

### Contents

INTRODUCTION | 3 |

PRELIMINARIES | 16 |

2 A Jensen type inequality for the nondecreasing rearrangement of nonnegative stochastic processes | 19 |

3 Continuity of Gaussian and subGaussian processes | 24 |

4 Sums of Banach space valued random variables | 40 |

RANDOM FOURIER SERIES ON LOCALLY COMPACT ABELIAN GROUPS | 51 |

2 Random Fourier series on the real line | 60 |

3 Random Fourier series on compact Abelian groups | 63 |

3 Continuity of random Fourier series | 93 |

APPLICATIONS TO HARMONIC ANALYSIS | 105 |

2 Applications to Sidon sets | 118 |

ADDITIONAL RESULTS AND COMMENTS | 122 |

2 Almost sure almost periodicity | 134 |

3 On left and right almost sure continuity | 138 |

4 Generalizations | 140 |

REFERENCES | 144 |

THE CENTRAL LIMIT THEOREM AND RELATED QUESTIONS | 65 |

RANDOM FOURIER SERIES ON COMPACT NONABELIAN GROUPS | 74 |

2 Random series with coefficients in a Banach space | 81 |

### Other editions - View all

Random Fourier Series with Applications to Harmonic Analysis Michael B. Marcus,Gilles Pisier No preview available - 1981 |

### Common terms and phrases

a.s. continuous a.s. with respect absolute constant assume B(Hj balls of radius Banach space central limit theorem Cg s G Chapter compact Abelian group compact group complete the proof continuous function continuous sample paths converges uniformly a.s. Corollary cotype defined denote distribution djtr equivalent Fernique finite dimensional Gaussian random variables Haar measure HARMONIC ANALYSIS Hilbert space I(ff implies independent copies inequality integral Lemma locally compact Abelian Math matrix mean zero metric entropy metric or pseudo-metric Moreover necessary and sufficient non-Abelian non-increasing norm notation obtain open balls Orlicz Orlicz space probability space proof of Theorem prove pseudo-metric Rademacher series random Fourier series random series REMARK resp satisfies the CLT sequence of independent series on compact Sidon sets sign-invariant stationary Gaussian processes sufficient condition sup sup Theorem 1.1 translation invariant metric uniform convergence a.s. valued random variables version with continuous Zygmund