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Integrability Theorems for Trigonometric Transforms

  • Book
  • © 1967

Overview

Authors:
  1. Ralph P. Boas

    1. Northwestern University, Evanston, USA

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Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge (MATHE2, volume 38)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-2
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  2. Introduction

    • Ralph P. Boas Jr.
    Pages 3-6

  3. Lemmas

    • Ralph P. Boas Jr.
    Pages 7-12

  4. Theorems with positive or decreasing functions

    • Ralph P. Boas Jr.
    Pages 13-18

  5. Theorems with positive or decreasing coefficients

    • Ralph P. Boas Jr.
    Pages 19-25

  6. The exceptional integral values of the index

    • Ralph P. Boas Jr.
    Pages 26-34

  7. LP problems, 1 < p < ∞

    • Ralph P. Boas Jr.
    Pages 35-42

  8. Asymptotic formulas and Lipschitz conditions

    • Ralph P. Boas Jr.
    Pages 43-51

  9. More general classes of functions; conditional convergence

    • Ralph P. Boas Jr.
    Pages 52-56

  10. Trigonometric integrals

    • Ralph P. Boas Jr.
    Pages 57-59

  11. Back Matter

    Pages 60-65
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Keywords

About this book

This monograph is areport on the present state of a fairly coherent collection of problems about which a sizeable literature has grown up in recent years. In this literature, some of the problems have, as it happens, been analyzed in great detail, whereas other very similar ones have been treated much more superficially. I have not attempted to improve on the literature by making equally detailed presentations of every topic. I have also not aimed at encyclopedic completeness. I have, however, pointed out some possible generalizations by stating a number of questions; some of these could doubtless be disposed of in a few minutes; some are probably quite difficult. This monograph was written at the suggestion of B. SZ.-NAGY. I take this opportunity of pointing out that his paper [1] inspired the greater part of the material that is presented here; in particular, it contains the happy idea of focusing Y attention on the multipliers nY-i, x- . R. ASKEY, P. HEYWOOD, M. and S. IZUMI, and S. WAINGER have kindly communicated some of their recent results to me before publication. I am indebted for help on various points to L. S. BOSANQUET, S. M. EDMONDS, G. GOES, S. IZUMI, A. ZYGMUND, and especially to R. ASKEY. My work was supported by the National Science Foundation under grants GP-314, GP-2491, GP-3940 and GP-5558. Evanston, Illinois, February, 1967 R. P. Boas, Jr. Contents Notations ... § 1. Introduetion 3 §2. Lemmas .. 7 § 3. Theorems with positive or decreasing functions .

Authors and Affiliations

  • Northwestern University, Evanston, USA

    Ralph P. Boas

Bibliographic Information

  • Book Title: Integrability Theorems for Trigonometric Transforms

  • Authors: Ralph P. Boas

  • Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge

  • DOI: https://doi.org/10.1007/978-3-642-87108-5

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin · Heidelberg 1967

  • Softcover ISBN: 978-3-642-87110-8Published: 03 May 2012

  • eBook ISBN: 978-3-642-87108-5Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: VIII, 66

  • Topics: Geometry

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