02984cam a2200349 a 4500 16826580 OSt 20170123094008.0 110614s2011 njua b 001 0 eng 2011020971 9780691113876 (alk. paper) 0691113874 DLC DLC DLC pcc QA320 .S839 2011 515.7 23 SEF MAT037000 bisacsh Stein, Elias M., 1931- 45916 Functional analysis : introduction to further topics in analysis / Elias M. Stein & Rami Shakarchi. Princeton : Princeton University Press, c2011. xv, 423 p. : ill. ; 24 cm. Princeton lectures in analysis ; 4 Includes bibliographical references (p.409-416) and index. "This 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" -- "This book covers such topics as Lp spaces, distributions, Baire category, probability theory and Brownian motion, several complex variables and oscillatory integrals in Fourier analysis. The authors focus on key results in each area, highlighting their importance and the organic unity of the subject"-- Functional analysis. 4418 MATHEMATICS / Functional Analysis. bisacsh 45917 Shakarchi, Rami. 45918 7 cbc orignew 1 ecip 20 y-gencatlg ddc BOOK 35394 269894 0 2014-07-07 0 0 515.7 SEF 2014-07-07 CL 00651805 CL 2014-07-07 00:00:00 BOOK ddc 0 0 2014-07-07 0 0 515.7 SEF 2014-07-07 CL 00651806 CL 2014-07-07 00:00:00 BOOK ddc 0 0 2014-07-07 0 0 515.7 SEF 2014-07-07 CL 00651807 CL 2014-07-07 00:00:00 BOOK ddc 0 0 2014-07-07 0 0 515.7 SEF 2014-07-07 EZF 00651808 EZF 2016-06-02 2016-06-02 00:00:00 BOOK ddc 1 0 2014-07-07 0 0 515.7 SEF 2014-07-07 SZM 00651809 SZM 2014-07-07 00:00:00 BOOK ddc 0 0 2017-08-04 0 0 515.7 SEF 2017-08-04 EZF 00656353 EZF 2017-08-04 00:00:00 BOOK ddc 0 0 2017-08-04 0 0 515.7 SEF 2017-08-04 SZM 00656399 SZM 2017-08-04 00:00:00 BOOK ddc 0