Integrability Theorems for Trigonometric Transforms (Paperback)

Ralph P.JR. Boas

ISBN 10: 3642871100 / ISBN 13: 9783642871108

Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin, 2012

Riguardo questo articolo

Paperback. 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 . 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. I take this opportunity of pointing out that his paper [1] inspired the greater part of the material that is presented here; Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Codice articolo 9783642871108

Dati bibliografici

• Titolo: Integrability Theorems for Trigonometric Transforms (Paperback)
• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 3642871100
• ISBN 13: 9783642871108
• Rilegatura: Paperback
• Condizione: new

Descrizione articolo

Riassunto

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 .

Contenuti

§ 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.