Harmonic Analysis and the Theory of Probability

Author: Salomon Bochner

Publisher: Courier Corporation

ISBN: 0486154807

Category: Mathematics

Page: 192

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Written by a distinguished mathematician and educator, this classic text emphasizes stochastic processes and the interchange of stimuli between probability and analysis. It also introduces the author's innovative concept of the characteristic functional. 1955 edition.

Fourier Analysis on Groups

Author: Walter Rudin

Publisher: Courier Dover Publications

ISBN: 0486821013

Category: Mathematics

Page: 304

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Written by a master mathematical expositor, this classic text reflects the results of the intense period of research and development in the area of Fourier analysis in the decade preceding its first publication in 1962. The enduringly relevant treatment is geared toward advanced undergraduate and graduate students and has served as a fundamental resource for more than five decades. The self-contained text opens with an overview of the basic theorems of Fourier analysis and the structure of locally compact Abelian groups. Subsequent chapters explore idempotent measures, homomorphisms of group algebras, measures and Fourier transforms on thin sets, functions of Fourier transforms, closed ideals in L1(G), Fourier analysis on ordered groups, and closed subalgebras of L1(G). Helpful Appendixes contain background information on topology and topological groups, Banach spaces and algebras, and measure theory.

Introduction to Banach Spaces: Analysis and Probability:

Author: Daniel Li,Hervé Queffélec

Publisher: Cambridge University Press

ISBN: 1108298168

Category: Mathematics

Page: N.A

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This two-volume text provides a complete overview of the theory of Banach spaces, emphasising its interplay with classical and harmonic analysis (particularly Sidon sets) and probability. The authors give a full exposition of all results, as well as numerous exercises and comments to complement the text and aid graduate students in functional analysis. The book will also be an invaluable reference volume for researchers in analysis. Volume 1 covers the basics of Banach space theory, operatory theory in Banach spaces, harmonic analysis and probability. The authors also provide an annex devoted to compact Abelian groups. Volume 2 focuses on applications of the tools presented in the first volume, including Dvoretzky's theorem, spaces without the approximation property, Gaussian processes, and more. Four leading experts also provide surveys outlining major developments in the field since the publication of the original French edition.

The Stanford Mathematics Problem Book

With Hints and Solutions

Author: George Pólya,Jeremy Kilpatrick

Publisher: Courier Corporation

ISBN: 0486469247

Category: Mathematics

Page: 68

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Based on Stanford University's well-known competitive exam, this excellent mathematics workbook offers students at both high school and college levels a complete set of problems, hints, and solutions. 1974 edition.

Probabilities on Algebraic Structures

Author: Ulf Grenander

Publisher: Courier Corporation

ISBN: 0486462870

Category: Mathematics

Page: 218

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This systematic approach covers semi-groups, groups, linear vector spaces, and algebra. It states and studies fundamental probabilistic problems for these spaces, focusing on concrete results. 1963 edition.

Information Theory

Author: Robert B. Ash

Publisher: Courier Corporation

ISBN: 9780486665214

Category: Mathematics

Page: 339

View: 1681

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Developed by Claude Shannon and Norbert Wiener in the late Forties, information theory, or statistical communication theory, deals with the theoretical underpinnings of a wide range of communication devices: radio, television, radar, computers, telegraphy, and more. This book is an excellent introduction to the mathematics underlying the theory. Designed for upper-level undergraduates and first-year graduate students, the book treats three major areas: analysis of channel models and proof of coding theorems (Chapters 3, 7 and 8); study of specific coding systems (Chapters 2, 4, and 5); and study of statistical properties of information sources (Chapter 6). Among the topics covered are noiseless coding, the discrete memoryless channel, error correcting codes, information sources, channels with memory and continuous channels. The author has tried to keep the prerequisites to a minimum. However, students should have a knowledge of basic probability theory. Some measure and Hilbert space theory is helpful as well for the last two sections of Chapter 8, which treat time-continuous channels. An appendix summarizes the Hilbert space background and the results from the theory of stochastic processes necessary for these sections. The appendix is not self-contained, but will serve to pinpoint some of the specific equipment needed for the analysis of time-continuous channels. In addition to historic notes at the end of each chapter indicating the origin of some of the results, the author has also included 60 problems, with detailed solutions, making the book especially valuable for independent study.

An Introduction to Lebesgue Integration and Fourier Series

Author: Howard J. Wilcox,David L. Myers

Publisher: Courier Corporation

ISBN: 9780486682938

Category: Mathematics

Page: 159

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This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects. The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the student's repertoire. Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration.

The Theory of Graphs

Author: Claude Berge

Publisher: Courier Corporation

ISBN: 9780486419756

Category: Mathematics

Page: 247

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Concise, well-written text illustrates development of graph theory and application of its principles in methods both formal and abstract. Practical examples explain theory's broad range, from behavioral sciences, information theory, cybernetics, and other areas, to mathematical disciplines such as set and matrix theory. 1966 edition. Includes 109 black-and-white illustrations.

Challenging Mathematical Problems with Elementary Solutions

Author: A. M. Yaglom,I. M. Yaglom

Publisher: Courier Corporation

ISBN: 0486318575

Category: Mathematics

Page: 239

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Volume I of a two-part series, this book features a broad spectrum of 100 challenging problems related to probability theory and combinatorial analysis. Most can be solved with elementary mathematics. Complete solutions.

An Introduction to the Theory of Stationary Random Functions

Author: A. M. Yaglom

Publisher: Courier Corporation

ISBN: 9780486495712

Category: Mathematics

Page: 235

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This two-part treatment covers the general theory of stationary random functions and the Wiener-Kolmogorov theory of extrapolation and interpolation of random sequences and processes. Beginning with the simplest concepts, it covers the correlation function, the ergodic theorem, homogenous random fields, and general rational spectral densities, among other topics. Numerous examples appear throughout the text, with emphasis on the physical meaning of mathematical concepts. Although rigorous in its treatment, this is essentially an introduction, and the sole prerequisites are a rudimentary knowledge of probability and complex variable theory. 1962 edition.

Special Functions & Their Applications

Author: N. N. Lebedev

Publisher: Courier Corporation

ISBN: 0486139891

Category: Mathematics

Page: 308

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Famous Russian work discusses the application of cylinder functions and spherical harmonics; gamma function; probability integral and related functions; Airy functions; hyper-geometric functions; more. Translated by Richard Silverman.

Applied Mathematics for Engineers and Physicists

Third Edition

Author: Louis A. Pipes,Lawrence R. Harvill

Publisher: Courier Corporation

ISBN: 0486794997

Category: Mathematics

Page: 1040

View: 2079

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Suitable for advanced courses in applied mathematics, this text covers analysis of lumped parameter systems, distributed parameter systems, and important areas of applied mathematics. Answers to selected problems. 1970 edition.

Analysis II

Author: Herbert Amann,Joachim Escher

Publisher: Springer Science & Business Media

ISBN: 3764371056

Category: Mathematics

Page: 415

View: 4999

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Der zweite Band dieser Einführung in die Analysis behandelt die Integrationstheorie von Funktionen einer Variablen, die mehrdimensionale Differentialrechnung und die Theorie der Kurven und Kurvenintegrale. Der im ersten Band begonnene moderne und klare Aufbau wird konsequent fortgesetzt. Dadurch wird ein tragfähiges Fundament geschaffen, das es erlaubt, interessante Anwendungen zu behandeln, die zum Teil weit über den in der üblichen Lehrbuchliteratur behandelten Stoff hinausgehen. Zahlreiche Übungsaufgaben von unterschiedlichem Schwierigkeitsgrad und viele informative Abbildungen runden dieses Lehrbuch ab.

Fundamentals of Modern Mathematics

A Practical Review

Author: David B. MacNeil

Publisher: Courier Corporation

ISBN: 0486316149

Category: Mathematics

Page: 320

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Students and others wishing to know more about the practical side of mathematics will find this volume a highly informative resource. Accessible explanations of important concepts feature worked examples and diagrams. 1963 edition.

Great Currents of Mathematical Thought

Marthematics in the Arts and Sciences

Author: François Le Lionnais

Publisher: Courier Corporation

ISBN: 9780486495798

Category: Mathematics

Page: 266

View: 9203

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50 essays by eminent scholars include meditations on "Structures," Disciplines," "Space," "Function," "Group," "Probability," and "The Mathematical Epic" (Volume I) and on "Mathematics and the Human Intellect," "Mathematics and Technology," and "Mathematics and Civilization" (Volume II). 1962 edition.

Fourier Series

Author: Georgi? Pavlovich Tolstov,Richard A. Silverman

Publisher: Courier Corporation

ISBN: 9780486633176

Category: Mathematics

Page: 336

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Richard A. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in the fields of mathematics, physics, and engineering. The present book is another excellent text from this series, a valuable addition to the English-language literature on Fourier series. This edition is organized into nine well-defined chapters: Trigonometric Fourier Series, Orthogonal Systems, Convergence of Trigonometric Fourier Series, Trigonometric Series with Decreasing Coefficients, Operations on Fourier Series, Summation of Trigonometric Fourier Series, Double Fourier Series and the Fourier Integral, Bessel Functions and Fourier-Bessel Series, and the Eigenfunction Method and its Applications to Mathematical Physics. Every chapter moves clearly from topic to topic and theorem to theorem, with many theorem proofs given. A total of 107 problems will be found at the ends of the chapters, including many specially added to this English-language edition, and answers are given at the end of the text. Richard Silverman's excellent translation makes this book readily accessible to mathematicians and math students, as well as workers and students in the fields of physics and engineering. He has also added a bibliography, containing suggestions for collateral and supplementary reading. 1962 edition.

How to Solve Applied Mathematics Problems

Author: B. L. Moiseiwitsch

Publisher: Courier Corporation

ISBN: 0486285227

Category: Mathematics

Page: 336

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This workbook bridges the gap between lectures and practical applications, offering students of mathematics, engineering, and physics the chance to practice solving problems from a wide variety of fields. 2011 edition.

The Convolution Transform

Author: Isidore Isaac Hirschman,David V. Widder

Publisher: Courier Corporation

ISBN: 0486154564

Category: Mathematics

Page: 288

View: 1282

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The relation between differential operators and integral transforms is the theme of this work. Discusses finite and non-finite kernels, variation diminishing transforms, asymptotic behavior of kernels, real inversion theory, representation theory, the Weierstrass transform, more.