02851nmm a2200277 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002100139245010200160250001700262260006300279300003200342505039500374653001300769653001300782710003400795041001900829989003800848490010600886856007200992082000801064520150101072EB000678206EBX0100000000000000053128800000000000000.0cr|||||||||||||||||||||140122 ||| eng a97836428710851 aBoas, Ralph P.Jr00aIntegrability Theorems for Trigonometric TransformshElektronische Ressourcecby Ralph P.Jr. Boas a1st ed. 1967 aBerlin, HeidelbergbSpringer Berlin Heidelbergc1967, 1967 aVIII, 66 pbonline resource0 a§ 1. Introduction -- § 2. Lemmas -- § 3. Theorems with positive or decreasing functions -- § 4. Theorems with positive or decreasing coefficients -- § 5. The exceptional integral values of the index -- § 6. Lp problems, 1 < p < ? -- § 7. Asymptotic formulas and Lipschitz conditions -- § 8. More general classes of functions; conditional convergence -- § 9. Trigonometric integrals aGeometry aGeometry2 aSpringerLink (Online service)07aeng2ISO 639-2 bSBAaSpringer Book Archives -20040 aErgebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics uhttps://doi.org/10.1007/978-3-642-87108-5?nosfx=yxVerlag3Volltext0 a516 aThis 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