Ralph P.Jr. Boas's Books

Integrability Theorems for Trigonometric Transforms

By: Ralph P.Jr. Boas

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Integrability Theorems for Trigonometric Transforms

By: Ralph P.Jr. Boas

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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Springer Science & Business Media

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ISBN 10

3642871089

ISBN 13

9783642871085

Polynomial Expansions of Analytic Functions

Reihe: Moderne Funktionentheorie

By: Ralph P.Jr. Boas,R.C. Buck

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Polynomial Expansions of Analytic Functions

Reihe: Moderne Funktionentheorie

By: Ralph P.Jr. Boas,R.C. Buck

This monograph deals with the expansion properties, in the complex domain, of sets of polynomials which are defined by generating relations. It thus represents a synthesis of two branches of analysis which have been developing almost independently. On the one hand there has grown up a body of results dealing with the more or less formal prop erties of sets of polynomials which possess simple generating relations. Much of this material is summarized in the Bateman compendia (ERDELYI [1J, vol. III, chap. 19) and in TRUESDELL [1J. On the other hand, a problem of fundamental interest in classical analysis is to study the representability of an analytic function j(z) as a series 2::CnPn(z), where {Pn} is a prescribed sequence of functions, and the connections between the function j and the coefficients en. BIEBERBACH'S mono graph Analytisehe Fortsetzung (Ergebnisse der Mathematik, new series, no. 3) can be regarded as a study of this problem for the special choice Pn (z) = zn, and illustrates the depth and detail which such a specializa tion allows. However, the wealth of available information about other sets of polynomials has seldom been put to work in this connection (the application of generating relations to expansion of functions is not even mentioned in the Bateman compendia). At the other extreme, J. M.

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Springer Science & Business Media

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ISBN 10

3642878873

ISBN 13

9783642878879

Land of the Elms

By: Ralph Cross

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Land of the Elms

By: Ralph Cross

Thirteen-year-old George Scott experiences one crisis after another in the action-packed Land of the Elms, which is set during the Oklahoma Land Rush and is historically accurate. George is embroiled in a series of events starting with his father coming home with a Flint Road Cart to be pulled by their horse so that George can be part of the historic event. Once they leave home, George rescues a wealthy heiress, becomes involved with con men who want to kill him, pushes on to the selected land alone when his father breaks his leg, is tricked by a woman he befriended, is caught in a tornado, and learns that the elms land is so sought after because it has rich soil. Surviving every challenge, George learns in the end that aThere really is more than one way to win a horse race.a

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218

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Publishamerica Incorporated

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ISBN 10

1607031035

ISBN 13

9781607031031

Book's by Ralph P.Jr. Boas

Integrability Theorems for Trigonometric Transforms

Integrability Theorems for Trigonometric Transforms

Polynomial Expansions of Analytic Functions

Polynomial Expansions of Analytic Functions

Land of the Elms

Land of the Elms

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