Boas, Ralph P. (Ralph Philip) 19121992
Overview
Works:  41 works in 319 publications in 5 languages and 7,115 library holdings 

Genres:  Dictionaries Miscellanea Filmed lectures Nonfiction films Filmed speeches 
Roles:  Author, Editor, Translator, Other 
Classifications:  QA331, 517.5 
Publication Timeline
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Most widely held works by
Ralph P Boas
A primer of real functions by
Ralph P Boas(
Book
)
85 editions published between 1960 and 1997 in 3 languages and held by 2,107 WorldCat member libraries worldwide
"This is a revised, updated, and augmented edition of a classic Carus monograph with a new chapter on integration and its applications. Earlier editions covered sets, metric spaces, continuous functions, and differentiable functions. To that, this edition adds sections on measurable sets and functions and the Lebesgue and Stieltjes integrals. The book retains the informal chatty style of the previous editions. It presents a variety of interesting topics, many of which are not commonly encountered in undergraduate textbooks, such as the existence of continuous everywhereoscillating functions; two functions having equal derivatives, yet not differing by a constant; application of Stieltjes integration to the speed of convergence of infinite series. For readers with a background in calculus, the book is suitable either for selfstudy or for supplemental reading in a course on advanced calculus or real analysis. Students of mathematics will find here the sense of wonder that was associated with the subject in its early days"Publisher description
85 editions published between 1960 and 1997 in 3 languages and held by 2,107 WorldCat member libraries worldwide
"This is a revised, updated, and augmented edition of a classic Carus monograph with a new chapter on integration and its applications. Earlier editions covered sets, metric spaces, continuous functions, and differentiable functions. To that, this edition adds sections on measurable sets and functions and the Lebesgue and Stieltjes integrals. The book retains the informal chatty style of the previous editions. It presents a variety of interesting topics, many of which are not commonly encountered in undergraduate textbooks, such as the existence of continuous everywhereoscillating functions; two functions having equal derivatives, yet not differing by a constant; application of Stieltjes integration to the speed of convergence of infinite series. For readers with a background in calculus, the book is suitable either for selfstudy or for supplemental reading in a course on advanced calculus or real analysis. Students of mathematics will find here the sense of wonder that was associated with the subject in its early days"Publisher description
Polynomial expansions of analytic functions by
Ralph P Boas(
Book
)
47 editions published between 1958 and 1964 in 4 languages and held by 774 WorldCat member libraries worldwide
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 [1], voi. III, chap. 19) and in TRUESDELL [1]. On the other hand, a problem of fundamental interest in classical analysis is to study the representability of an analytic function f(z) as a series ,Lc,. p,. (z), where {p,. } is a prescribed sequence of functions, and the connections between the function f and the coefficients c,. . BIEBERBACH's mono graph Analytische Fortsetzung (Ergebnisse der Mathematik, new series, no. 3) can be regarded as a study of this problem for the special choice p,. (z) =z", 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
47 editions published between 1958 and 1964 in 4 languages and held by 774 WorldCat member libraries worldwide
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 [1], voi. III, chap. 19) and in TRUESDELL [1]. On the other hand, a problem of fundamental interest in classical analysis is to study the representability of an analytic function f(z) as a series ,Lc,. p,. (z), where {p,. } is a prescribed sequence of functions, and the connections between the function f and the coefficients c,. . BIEBERBACH's mono graph Analytische Fortsetzung (Ergebnisse der Mathematik, new series, no. 3) can be regarded as a study of this problem for the special choice p,. (z) =z", 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
Entire functions by
Ralph P Boas(
Book
)
30 editions published between 1954 and 1973 in 3 languages and held by 713 WorldCat member libraries worldwide
30 editions published between 1954 and 1973 in 3 languages and held by 713 WorldCat member libraries worldwide
Invitation to complex analysis by
Ralph P Boas(
Book
)
19 editions published between 1987 and 2010 in English and held by 655 WorldCat member libraries worldwide
Ideal for a first course in complex analysis, this book can be used either as a classroom text or for independent study. Written at a level accessible to advanced undergraduates and beginning graduate students, the book is suitable for readers acquainted with advanced calculus or introductory real analysis. The treatment goes beyond the standard material of power series, Cauchy's theorem, residues, conformal mapping, and harmonic functions by including accessible discussions of intriguing topics that are uncommon in a book at this level. The flexibility afforded by the supplementary topics and applications makes the book adaptable either to a short, oneterm course or to a comprehensive, fullyear course. Detailed solutions of the exercises both serve as models for students and facilitate independent study. Supplementary exercises, not solved in the book, provide an additional teaching tool
19 editions published between 1987 and 2010 in English and held by 655 WorldCat member libraries worldwide
Ideal for a first course in complex analysis, this book can be used either as a classroom text or for independent study. Written at a level accessible to advanced undergraduates and beginning graduate students, the book is suitable for readers acquainted with advanced calculus or introductory real analysis. The treatment goes beyond the standard material of power series, Cauchy's theorem, residues, conformal mapping, and harmonic functions by including accessible discussions of intriguing topics that are uncommon in a book at this level. The flexibility afforded by the supplementary topics and applications makes the book adaptable either to a short, oneterm course or to a comprehensive, fullyear course. Detailed solutions of the exercises both serve as models for students and facilitate independent study. Supplementary exercises, not solved in the book, provide an additional teaching tool
Integrability theorems for trigonometric transforms by
Ralph P Boas(
Book
)
22 editions published in 1967 in 3 languages and held by 498 WorldCat member libraries worldwide
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 nYi, 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 GP314, GP2491, GP3940 and GP5558. Evanston, Illinois, February, 1967 R.P. Boas, Jr. Contents Notations ... ʹ 1. Introduetion 3 ʹ2. Lemmas .. 7 ʹ 3. Theorems with positive or decreasing functions
22 editions published in 1967 in 3 languages and held by 498 WorldCat member libraries worldwide
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 nYi, 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 GP314, GP2491, GP3940 and GP5558. Evanston, Illinois, February, 1967 R.P. Boas, Jr. Contents Notations ... ʹ 1. Introduetion 3 ʹ2. Lemmas .. 7 ʹ 3. Theorems with positive or decreasing functions
Lion hunting & other mathematical pursuits : a collection of mathematics, verse, and stories by
Ralph P Boas(
Book
)
8 editions published between 1994 and 1996 in English and held by 498 WorldCat member libraries worldwide
8 editions published between 1994 and 1996 in English and held by 498 WorldCat member libraries worldwide
Collected works by
Hidehiko Yamabe(
Book
)
12 editions published in 1967 in English and Undetermined and held by 293 WorldCat member libraries worldwide
12 editions published in 1967 in English and Undetermined and held by 293 WorldCat member libraries worldwide
RussianEnglish dictionary of the mathematical sciences by
A. J Lohwater(
Book
)
9 editions published in 1990 in English and Russian and held by 279 WorldCat member libraries worldwide
9 editions published in 1990 in English and Russian and held by 279 WorldCat member libraries worldwide
Introduction to the classical theory of Abelian functions by
A. I Markushevich(
Book
)
4 editions published in 1992 in English and held by 272 WorldCat member libraries worldwide
4 editions published in 1992 in English and held by 272 WorldCat member libraries worldwide
Probability by
Alʹbert Nikolaevich Shiri︠a︡ev(
Book
)
7 editions published between 1984 and 1996 in English and held by 75 WorldCat member libraries worldwide
This new edition contains substantial revisions and updated references. The reader will find a deeper study of topics such as the distance between probability measures, metrization of weak convergence, and contiguity of probability measures. Proofs for a number of some important results which were merely stated in the first edition have been added. The author has included new material on the probability of large deviations, on the central limit theorem for sums of dependent random variables, and on a discrete version of Ito's formula
7 editions published between 1984 and 1996 in English and held by 75 WorldCat member libraries worldwide
This new edition contains substantial revisions and updated references. The reader will find a deeper study of topics such as the distance between probability measures, metrization of weak convergence, and contiguity of probability measures. Proofs for a number of some important results which were merely stated in the first edition have been added. The author has included new material on the probability of large deviations, on the central limit theorem for sums of dependent random variables, and on a discrete version of Ito's formula
A manual for translators of mathematical Russian by
Sydney H Gould(
Book
)
5 editions published in 1991 in English and held by 54 WorldCat member libraries worldwide
5 editions published in 1991 in English and held by 54 WorldCat member libraries worldwide
Indeterminate forms revisited by
Ralph P Boas(
Visual
)
4 editions published between 1989 and 2009 in English and held by 37 WorldCat member libraries worldwide
Ralph P. Boas sketches some of the history of the famous theorem of l'Hopital of elementary calculus, gives some advantages of various proofs, and discusses the fact that the role of integration can be played by a general linear operator that is the inverse of a differential operator, such as a Laplace transform
4 editions published between 1989 and 2009 in English and held by 37 WorldCat member libraries worldwide
Ralph P. Boas sketches some of the history of the famous theorem of l'Hopital of elementary calculus, gives some advantages of various proofs, and discusses the fact that the role of integration can be played by a general linear operator that is the inverse of a differential operator, such as a Laplace transform
Orthogonal series by
B. S Kashin(
Book
)
2 editions published in 1989 in English and held by 25 WorldCat member libraries worldwide
2 editions published in 1989 in English and held by 25 WorldCat member libraries worldwide
Limits of indeterminacy in measure of trigonometric and orthogonal series by
D. E Menʹshov(
Book
)
2 editions published in 1968 in English and held by 22 WorldCat member libraries worldwide
2 editions published in 1968 in English and held by 22 WorldCat member libraries worldwide
Foundations of game theory : noncooperative games by
N. N Vorobʹev(
Book
)
3 editions published in 1994 in English and held by 9 WorldCat member libraries worldwide
3 editions published in 1994 in English and held by 9 WorldCat member libraries worldwide
George Polya, collected papers by
George Pólya(
Book
)
3 editions published between 1974 and 2003 in English and Undetermined and held by 4 WorldCat member libraries worldwide
3 editions published between 1974 and 2003 in English and Undetermined and held by 4 WorldCat member libraries worldwide
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Related Identities
 Boas, Harold P. Other Contributor Editor
 Buck, R. Creighton (Robert Creighton) 1920
 Mugler, Dale H.
 Alexanderson, Gerald L. Author
 Yamabe, Hidehiko 19231960 Author
 Lohwater, A. J. Author
 Thorpe, Alana I. Other
 Markushevich, A. I. (Alekseĭ Ivanovich) 1908 Author
 Širâev, Alʹbert Nikolaevič 1934 ... Author
 Pólya, George 18871985 Author
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Associated Subjects
Analytic functions Calculus Combinatorial analysis Diophantine equations Distribution (Probability theory) Economics EducationCurricula English languageTranslating into Russian Forms (Mathematics) Fourier series Functional analysis Functions Functions, Abelian Functions, Entire Functions of complex variables Functions of real variables Global analysis (Mathematics) Harvard University Laplace transformation Linear operators Mathematical analysis Mathematical optimization Mathematics MathematicsTranslating Measure theory Noncooperative games (Mathematics) Polynomials Probabilities Russian language Russian languageTechnical Russian Russian languageTranslating Russian languageTranslating into English Series, Orthogonal Topological groups
Alternative Names
Boas, R. P.
Boas, R. P. 19121992
Boas, R. P. (Ralph Philip)
Boas, R. P. (Ralph Philip), 19121992
Boas, Ralph P.
Boas, Ralph P. 19121992
Boas, Ralph P. Jr
Boas, Ralph Philip
Boas, Ralph Philip 19121992
Ralph Boas USamerikanischer Mathematiker
Ralph P. Boas, Jr. Amerikaans wiskundige (19121992)
Ralph Philip Boas mathématicien américain
رالف فیلیپ بواس ریاضیدان آمریکایی
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