Integrability Theorems For Trigonometric Transforms

Author : Ralph P.Jr. Boas
Publisher : Springer Science & Business Media
ISBN 13 : 3642871089
Total Pages : 71 pages
Book Rating : 4.85/5 ( download)

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Download or read book Integrability Theorems for Trigonometric Transforms written by Ralph P.Jr. Boas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 .

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Publisher :
ISBN 13 :
Total Pages : 65 pages
Book Rating : 4.56/5 ( download)

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Download or read book Integrability theorems for trigonometric transforms written by and published by . This book was released on 1967 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Ralph Philip Boas
Publisher :
ISBN 13 :
Total Pages : 65 pages
Book Rating : 4.39/5 ( download)

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Download or read book Intregrability Theorems for Trigonometric Transforms written by Ralph Philip Boas and published by . This book was released on 1967 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Ralph P. Boas Jr.
Publisher : American Mathematical Soc.
ISBN 13 : 088385323X
Total Pages : 308 pages
Book Rating : 4.38/5 ( download)

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Download or read book Lion Hunting & Other Mathematical Pursuits: A Collection of Mathematics, Verse and Stories written by Ralph P. Boas Jr. and published by American Mathematical Soc.. This book was released on 2020-07-31 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the famous paper of 1938, “A Contribution to the Mathematical Theory of Big Game Hunting”, written by Ralph Boas along with Frank Smithies, using the pseudonym H. Pétard, Boas describes sixteen methods for hunting a lion. This marvelous collection of Boas memorabilia contains not only the original article, but also several additional articles, as late as 1985, giving many further methods. But once you are through with lion hunting, you can hunt through the remainder of the book to find numerous gems by and about this remarkable mathematician. Not only will you find his biography of Bourbaki along with a description of his feud with the French mathematician, but also you will find a lucid discussion of the mean value theorem. There are anecdotes Boas told about many famous mathematicians, along with a large collection of his mathematical verses. You will find mathematical articles like a proof of the fundamental theorem of algebra and pedagogical articles giving Boas' views on making mathematics intelligible.

Author : W.Y. Hsiang
Publisher : Springer Science & Business Media
ISBN 13 : 3642660525
Total Pages : 175 pages
Book Rating : 4.28/5 ( download)

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Download or read book Cohomology Theory of Topological Transformation Groups written by W.Y. Hsiang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historically, applications of algebraic topology to the study of topological transformation groups were originated in the work of L. E. 1. Brouwer on periodic transformations and, a little later, in the beautiful fixed point theorem ofP. A. Smith for prime periodic maps on homology spheres. Upon comparing the fixed point theorem of Smith with its predecessors, the fixed point theorems of Brouwer and Lefschetz, one finds that it is possible, at least for the case of homology spheres, to upgrade the conclusion of mere existence (or non-existence) to the actual determination of the homology type of the fixed point set, if the map is assumed to be prime periodic. The pioneer result of P. A. Smith clearly suggests a fruitful general direction of studying topological transformation groups in the framework of algebraic topology. Naturally, the immediate problems following the Smith fixed point theorem are to generalize it both in the direction of replacing the homology spheres by spaces of more general topological types and in the direction of replacing the group tl by more general compact groups.

Author : P.L. Butzer
Publisher : Birkhäuser
ISBN 13 : 3034874480
Total Pages : 565 pages
Book Rating : 4.89/5 ( download)

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Download or read book Fourier Analysis and Approximation written by P.L. Butzer and published by Birkhäuser. This book was released on 2012-12-06 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the international conference on 'Harmonic Analysis and Integral Transforms', conducted by one of the authors at the Mathematical Research Institute in Oberwolfach (Black Forest) in August 1965, it was felt that there was a real need for a book on Fourier analysis stressing (i) parallel treatment of Fourier series and Fourier trans forms from a transform point of view, (ii) treatment of Fourier transforms in LP(lRn)_ space not only for p = 1 and p = 2, (iii) classical solution of partial differential equations with completely rigorous proofs, (iv) theory of singular integrals of convolu tion type, (v) applications to approximation theory including saturation theory, (vi) multiplier theory, (vii) Hilbert transforms, Riesz fractional integrals, Bessel potentials, (viii) Fourier transform methods on locally compact groups. This study aims to consider these aspects, presenting a systematic treatment of Fourier analysis on the circle as well as on the infinite line, and of those areas of approximation theory which are in some way or other related thereto. A second volume is in preparation which goes beyond the one-dimensional theory presented here to cover the subject for functions of several variables. Approximately a half of this first volume deals with the theories of Fourier series and of Fourier integrals from a transform point of view.

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Publisher : Academic Press
ISBN 13 : 9780080873534
Total Pages : 554 pages
Book Rating : 4.37/5 ( download)

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Download or read book Fourier Analysis and Approximation written by and published by Academic Press. This book was released on 2011-09-21 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier Analysis and Approximation

Author : R. E. Edwards
Publisher : Springer Science & Business Media
ISBN 13 : 3642663664
Total Pages : 223 pages
Book Rating : 4.66/5 ( download)

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Download or read book Littlewood-Paley and Multiplier Theory written by R. E. Edwards and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to be a detailed and carefully written account of various versions of the Littlewood-Paley theorem and of some of its applications, together with indications of its general significance in Fourier multiplier theory. We have striven to make the presentation self-contained and unified, and adapted primarily for use by graduate students and established mathematicians who wish to begin studies in these areas: it is certainly not intended for experts in the subject. It has been our experience, and the experience of many of our students and colleagues, that this is an area poorly served by existing books. Their accounts of the subject tend to be either ill-suited to the needs of a beginner, or fragmentary, or, in one or two instances, obscure. We hope that our book will go some way towards filling this gap in the literature. Our presentation of the Littlewood-Paley theorem proceeds along two main lines, the first relating to singular integrals on locally com pact groups, and the second to martingales. Both classical and modern versions of the theorem are dealt with, appropriate to the classical n groups IRn, ?L , Tn and to certain classes of disconnected groups. It is for the disconnected groups of Chapters 4 and 5 that we give two separate accounts of the Littlewood-Paley theorem: the first Fourier analytic, and the second probabilistic.

Author : C. van den Berg
Publisher : Springer Science & Business Media
ISBN 13 : 3642661289
Total Pages : 205 pages
Book Rating : 4.80/5 ( download)

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Download or read book Potential Theory on Locally Compact Abelian Groups written by C. van den Berg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical potential theory can be roughly characterized as the study of Newtonian potentials and the Laplace operator on the Euclidean space JR3. It was discovered around 1930 that there is a profound connection between classical potential 3 theory and the theory of Brownian motion in JR . The Brownian motion is determined by its semigroup of transition probabilities, the Brownian semigroup, and the connection between classical potential theory and the theory of Brownian motion can be described analytically in the following way: The Laplace operator is the infinitesimal generator for the Brownian semigroup and the Newtonian potential kernel is the" integral" of the Brownian semigroup with respect to time. This connection between classical potential theory and the theory of Brownian motion led Hunt (cf. Hunt [2]) to consider general "potential theories" defined in terms of certain stochastic processes or equivalently in terms of certain semi groups of operators on spaces of functions. The purpose of the present exposition is to study such general potential theories where the following aspects of classical potential theory are preserved: (i) The theory is defined on a locally compact abelian group. (ii) The theory is translation invariant in the sense that any translate of a potential or a harmonic function is again a potential, respectively a harmonic function; this property of classical potential theory can also be expressed by saying that the Laplace operator is a differential operator with constant co efficients.

Author : Sylvia Weiser
Publisher :
ISBN 13 :
Total Pages : 234 pages
Book Rating : 4.35/5 ( download)

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Download or read book Guide to the Literature of Engineering, Mathematics, and the Physical Sciences written by Sylvia Weiser and published by . This book was released on 1972 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: