Introduction to Further Topics in Analysis Bk. 4
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Functional Analysis by Elias M. Stein
Book DescriptionThis is the fourth and final volume in the Princeton Lectures in Analysis, a series of textbooks that aim to present, in an integrated manner, the core areas of analysis. Beginning with the basic facts of functional analysis, this volume looks at Banach spaces, Lp spaces, and distribution theory, and highlights their roles in harmonic analysis. The authors then use the Baire category theorem to illustrate several points, including the existence of Besicovitch sets. The second half of the book introduces readers to other central topics in analysis, such as probability theory and Brownian motion, which culminates in the solution of Dirichlet's problem. The concluding chapters explore several complex variables and oscillatory integrals in Fourier analysis, and illustrate applications to such diverse areas as nonlinear dispersion equations and the problem of counting lattice points. Throughout the book, the authors focus on key results in each area and stress the organic unity of the subject. * A comprehensive and authoritative text that treats some of the main topics of modern analysis * A look at basic functional analysis and its applications in harmonic analysis, probability theory, and several complex variables * Key results in each area discussed in relation to other areas of mathematics * Highlights the organic unity of large areas of analysis traditionally split into subfields * Interesting exercises and problems illustrate ideas * Clear proofs provided
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Book DetailsISBN: 9780691113876
(229mm x 152mm x 36mm)
Imprint: Princeton University Press
Publisher: Princeton University Press
Publish Date: 15-Sep-2008
Country of Publication: United States
Books By Author Elias M. Stein
Lectures on Pseudo-Differential Operators: Regularity Theorems and Applications to Non-Elliptic Problems, Paperback (February 2015)
Real Analysis, Hardback (March 2005)» View all books by Elias M. Stein
Intended for the students interested in the disciplines of mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels, this third volume in a series of titles focuses on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals.
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Author Biography - Elias M. Stein
Elias M. Stein is the Albert Baldwin Dod Professor of Mathematics at Princeton University. Rami Shakarchi received his PhD in mathematics from Princeton University. They are the coauthors of "Complex Analysis, Fourier Analysis", and "Real Analysis" (all Princeton).
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