An Introduction to Lebesgue Integration and Fourier Series

Author: Howard J. Wilcox
Publisher: Courier Corporation
ISBN: 9780486682938
Format: PDF, Mobi
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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.

Integral Measure and Derivative

Author: G. E. Shilov
Publisher: Courier Corporation
ISBN: 0486165612
Format: PDF, Mobi
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This treatment examines the general theory of the integral, Lebesque integral in n-space, the Riemann-Stieltjes integral, and more. "The exposition is fresh and sophisticated, and will engage the interest of accomplished mathematicians." — Sci-Tech Book News. 1966 edition.

Lectures on Measure and Integration

Author: Harold Widom
Publisher: Courier Dover Publications
ISBN: 0486816591
Format: PDF, ePub, Mobi
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Well-known, concise lecture notes present fundamentals of the Lebesgue theory of integration and introduce some applications. Topics include measures, integration, theorems of Fubini, representations of measures, Lebesgue spaces, differentiation, Fourier series. 1969 edition.

Introduction to Analysis

Author: Maxwell Rosenlicht
Publisher: Courier Corporation
ISBN: 0486134687
Format: PDF, ePub, Mobi
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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.

Foundations of Mathematical Analysis

Author: Richard Johnsonbaugh
Publisher: Courier Corporation
ISBN: 0486134776
Format: PDF, Mobi
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Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.

Fourier Series

Author: G. H. Hardy
Publisher: Courier Corporation
ISBN: 0486316289
Format: PDF, Mobi
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Classic graduate-level text discusses the Fourier series in Hilbert space, examines further properties of trigonometrical Fourier series, and concludes with a detailed look at the applications of previously outlined theorems. 1956 edition.

Lebesgue Integration

Author: J.H. Williamson
Publisher: Courier Corporation
ISBN: 0486796736
Format: PDF, Docs
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Concise introduction to Lebesgue integration may be read by any student familiar with real variable theory and elementary calculus. Topics include sets and functions, Lebesgue measure, integrals, calculus, and general measures. 1962 edition.

Measure and Integral

Author: Richard L. Wheeden
Publisher: CRC Press
ISBN: 1498702902
Format: PDF, Kindle
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Now considered a classic text on the topic, Measure and Integral: An Introduction to Real Analysis provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then presenting a more general treatment based on abstract notions characterized by axioms and with less geometric content. Published nearly forty years after the first edition, this long-awaited Second Edition also: Studies the Fourier transform of functions in the spaces L1, L2, and Lp, 1 p Shows the Hilbert transform to be a bounded operator on L2, as an application of the L2 theory of the Fourier transform in the one-dimensional case Covers fractional integration and some topics related to mean oscillation properties of functions, such as the classes of Hölder continuous functions and the space of functions of bounded mean oscillation Derives a subrepresentation formula, which in higher dimensions plays a role roughly similar to the one played by the fundamental theorem of calculus in one dimension Extends the subrepresentation formula derived for smooth functions to functions with a weak gradient Applies the norm estimates derived for fractional integral operators to obtain local and global first-order Poincaré–Sobolev inequalities, including endpoint cases Proves the existence of a tangent plane to the graph of a Lipschitz function of several variables Includes many new exercises not present in the first edition This widely used and highly respected text for upper-division undergraduate and first-year graduate students of mathematics, statistics, probability, or engineering is revised for a new generation of students and instructors. The book also serves as a handy reference for professional mathematicians.