Harmonic Analysis and the Theory of Probability

Author: Salomon Bochner

Publisher: Courier Corporation

ISBN: 0486154807

Category: Mathematics

Page: 192

View: 1608

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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.

Probability Theory

A Concise Course

Author: Richard A. Silverman

Publisher: Courier Corporation

ISBN: 9780486635446

Category: Mathematics

Page: 148

View: 9251

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This clear exposition begins with basic concepts and moves on to combination of events, dependent events and random variables, Bernoulli trials and the De Moivre-Laplace theorem, and more. Includes 150 problems, many with answers.

Probabilities on Algebraic Structures

Author: Ulf Grenander

Publisher: Courier Corporation

ISBN: 0486462870

Category: Mathematics

Page: 218

View: 2875

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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.

An Introduction to Harmonic Analysis

Author: Yitzhak Katznelson

Publisher: Cambridge University Press

ISBN: 9780521543590

Category: Mathematics

Page: 314

View: 3988

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First published in 1968, An Introduction to Harmonic Analysis has firmly established itself as a classic text and a favorite for students and experts alike. Professor Katznelson starts the book with an exposition of classical Fourier series. The aim is to demonstrate the central ideas of harmonic analysis in a concrete setting, and to provide a stock of examples to foster a clear understanding of the theory. Once these ideas are established, the author goes on to show that the scope of harmonic analysis extends far beyond the setting of the circle group, and he opens the door to other contexts by considering Fourier transforms on the real line as well as a brief look at Fourier analysis on locally compact abelian groups. This new edition has been revised by the author, to include several new sections and a new appendix.

Analysis and Probability

Wavelets, Signals, Fractals

Author: Palle E. T. Jorgensen

Publisher: Springer Science & Business Media

ISBN: 0387330828

Category: Mathematics

Page: 280

View: 3274

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Combines analysis and tools from probability, harmonic analysis, operator theory, and engineering (signal/image processing) Interdisciplinary focus with hands-on approach, generous motivation and new pedagogical techniques Numerous exercises reinforce fundamental concepts and hone computational skills Separate sections explain engineering terms to mathematicians and operator theory to engineers Fills a gap in the literature

The Statistical Analysis of Experimental Data

Author: John Mandel

Publisher: Courier Corporation

ISBN: 048613959X

Category: Mathematics

Page: 432

View: 5071

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First half of book presents fundamental mathematical definitions, concepts, and facts while remaining half deals with statistics primarily as an interpretive tool. Well-written text, numerous worked examples with step-by-step presentation. Includes 116 tables.

Introduction to Analysis

Author: Maxwell Rosenlicht

Publisher: Courier Corporation

ISBN: 0486134687

Category: Mathematics

Page: 272

View: 1855

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Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.

Fourier Analysis on Finite Groups and Applications

Author: Audrey Terras

Publisher: Cambridge University Press

ISBN: 9780521457187

Category: Mathematics

Page: 442

View: 3588

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A friendly introduction to Fourier analysis on finite groups, accessible to undergraduates/graduates in mathematics, engineering and the physical sciences.

Mathematical Analysis of Physical Problems

Author: Philip Russell Wallace

Publisher: Courier Corporation

ISBN: 0486646769

Category: Science

Page: 616

View: 2213

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This mathematical reference for theoretical physics employs common techniques and concepts to link classical and modern physics. It provides the necessary mathematics to solve most of the problems. Topics include the vibrating string, linear vector spaces, the potential equation, problems of diffusion and attenuation, probability and stochastic processes, and much more. 1972 edition.

Theory of Linear Operations

Author: S. Banach

Publisher: Elsevier

ISBN: 9780080887203

Category: Mathematics

Page: 248

View: 6972

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This classic work by the late Stefan Banach has been translated into English so as to reach a yet wider audience. It contains the basics of the algebra of operators, concentrating on the study of linear operators, which corresponds to that of the linear forms a1x1 + a2x2 + ... + anxn of algebra. The book gathers results concerning linear operators defined in general spaces of a certain kind, principally in Banach spaces, examples of which are: the space of continuous functions, that of the pth-power-summable functions, Hilbert space, etc. The general theorems are interpreted in various mathematical areas, such as group theory, differential equations, integral equations, equations with infinitely many unknowns, functions of a real variable, summation methods and orthogonal series. A new fifty-page section (``Some Aspects of the Present Theory of Banach Spaces'') complements this important monograph.

An Elementary Introduction to the Theory of Probability

Author: Boris Vladimirovich Gnedenko,Aleksandr I?Akovlevich Khinchin

Publisher: Courier Corporation

ISBN: 9780486601557

Category: Mathematics

Page: 130

View: 801

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This compact volume equips the reader with all the facts and principles essential to a fundamental understanding of the theory of probability. It is an introduction, no more: throughout the book the authors discuss the theory of probability for situations having only a finite number of possibilities, and the mathematics employed is held to the elementary level. But within its purposely restricted range it is extremely thorough, well organized, and absolutely authoritative. It is the only English translation of the latest revised Russian edition; and it is the only current translation on the market that has been checked and approved by Gnedenko himself. After explaining in simple terms the meaning of the concept of probability and the means by which an event is declared to be in practice, impossible, the authors take up the processes involved in the calculation of probabilities. They survey the rules for addition and multiplication of probabilities, the concept of conditional probability, the formula for total probability, Bayes's formula, Bernoulli's scheme and theorem, the concepts of random variables, insufficiency of the mean value for the characterization of a random variable, methods of measuring the variance of a random variable, theorems on the standard deviation, the Chebyshev inequality, normal laws of distribution, distribution curves, properties of normal distribution curves, and related topics. The book is unique in that, while there are several high school and college textbooks available on this subject, there is no other popular treatment for the layman that contains quite the same material presented with the same degree of clarity and authenticity. Anyone who desires a fundamental grasp of this increasingly important subject cannot do better than to start with this book. New preface for Dover edition by B. V. Gnedenko.

Mathematics for the Physical Sciences

Author: Laurent Schwartz

Publisher: Courier Dover Publications

ISBN: 0486466620

Category: Mathematics

Page: 358

View: 8935

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Concise treatment of mathematical entities employs examples from the physical sciences. Topics include distribution theory, Fourier series, Laplace transforms, wave and heat conduction equations, and gamma and Bessel functions. 1966 edition.

Introductory Complex Analysis

Author: Richard A. Silverman

Publisher: Courier Corporation

ISBN: 0486318524

Category: Mathematics

Page: 400

View: 6189

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Shorter version of Markushevich's Theory of Functions of a Complex Variable, appropriate for advanced undergraduate and graduate courses in complex analysis. More than 300 problems, some with hints and answers. 1967 edition.

Introductory Real Analysis

Author: A. N. Kolmogorov,S. V. Fomin

Publisher: Courier Corporation

ISBN: 0486134741

Category: Mathematics

Page: 416

View: 8631

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Comprehensive, elementary introduction to real and functional analysis covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, more. 1970 edition.

Harmonic Analysis for Engineers and Applied Scientists

Updated and Expanded Edition

Author: Gregory S. Chirikjian,Alexander B. Kyatkin

Publisher: Courier Dover Publications

ISBN: 0486795640

Category: Mathematics

Page: 880

View: 7623

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Although the Fourier transform is among engineering's most widely used mathematical tools, few engineers realize that the extension of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. This self-contained approach, geared toward readers with a standard background in engineering mathematics, explores the widest possible range of applications to fields such as robotics, mechanics, tomography, sensor calibration, estimation and control, liquid crystal analysis, and conformational statistics of macromolecules. Harmonic analysis is explored in terms of particular Lie groups, and the text deals with only a limited number of proofs, focusing instead on specific applications and fundamental mathematical results. Forming a bridge between pure mathematics and the challenges of modern engineering, this updated and expanded volume offers a concrete, accessible treatment that places the general theory in the context of specific groups.

Real-Variable Methods in Harmonic Analysis

Author: Alberto Torchinsky

Publisher: Elsevier

ISBN: 1483268888

Category: Mathematics

Page: 474

View: 8617

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Real-Variable Methods in Harmonic Analysis deals with the unity of several areas in harmonic analysis, with emphasis on real-variable methods. Active areas of research in this field are discussed, from the Calderón-Zygmund theory of singular integral operators to the Muckenhoupt theory of Ap weights and the Burkholder-Gundy theory of good ? inequalities. The Calderón theory of commutators is also considered. Comprised of 17 chapters, this volume begins with an introduction to the pointwise convergence of Fourier series of functions, followed by an analysis of Cesàro summability. The discussion then turns to norm convergence; the basic working principles of harmonic analysis, centered around the Calderón-Zygmund decomposition of locally integrable functions; and fractional integration. Subsequent chapters deal with harmonic and subharmonic functions; oscillation of functions; the Muckenhoupt theory of Ap weights; and elliptic equations in divergence form. The book also explores the essentials of the Calderón-Zygmund theory of singular integral operators; the good ? inequalities of Burkholder-Gundy; the Fefferman-Stein theory of Hardy spaces of several real variables; Carleson measures; and Cauchy integrals on Lipschitz curves. The final chapter presents the solution to the Dirichlet and Neumann problems on C1-domains by means of the layer potential methods. This monograph is intended for graduate students with varied backgrounds and interests, ranging from operator theory to partial differential equations.

The Stanford Mathematics Problem Book

With Hints and Solutions

Author: George Pólya,Jeremy Kilpatrick

Publisher: Courier Corporation

ISBN: 0486469247

Category: Mathematics

Page: 68

View: 2801

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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.

General Theory of Functions and Integration

Author: Angus Ellis Taylor

Publisher: Courier Corporation

ISBN: 0486649881

Category: Mathematics

Page: 437

View: 6224

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Uniting a variety of approaches to the study of integration, a well-known professor presents a single-volume "blend of the particular and the general, of the concrete and the abstract." 1966 edition.