## The Fourier Integral and Certain of Its ApplicationsThe book is concerned principally with the Plancherel and Tauber theories as modified by other workers in the field, notably Wiener himself. Based on a course of lectures delivered at the University of Cambridge in 1932, it is divided into three separate groups of ideas. The first group deals with the Fourier transform and the Plancherel theorem. The second group treats the notion of an absolutely convergent Fourier series and of a Tauberian theorem. In the last group, Wiener deals with the concept of the spectrum. The final chapter is a lucid eposition of general harmonic analysis. |

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### Contents

The Nature of Harmonic Analysis | 1 |

The Properties of the Lebesgue Integral | 4 |

The RieszFischer Theorem | 27 |

Copyright | |

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### Common terms and phrases

absolutely convergent algebra analytic APPLICATIONS argument assume becomes belongs to Lg Bibliography bounded calculus chapter clearly coefficients Combining complete const constant contains continuous converges corresponding defined definition denumerable differential differs dominated equal equations equivalent established everywhere exists expression fact finite follows formula FOURIER INTEGRAL Fourier series Fourier transform function given groups harmonic analysis Hence holds increasing Index infinite interval introduction Lebesgue lemma less limit linear logic mathematical mean measurable methods modulus monotone null set obtain operator Paperbound particular pertaining points polynomial positive possible present problems proof proposition prove result sequence square symbolic Tauberian tends term theorem theory translation number true uniformly values vanish variable write zero