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- 000 02910cam a2200349 a 4500
- 008 130315r20132011cc a b 001 0 eng d
- 020 __ |a 9787510050350 (pbk.)
- 040 __ |a BUA |c BUA |d JLU |d SCT
- 050 _4 |a QA320 |b .S839 2011
- 099 __ |a CAL 022013012135
- 100 1_ |a Stein, Elias M., |d 1931-
- 245 10 |a Functional analysis : |b introduction to further topics in analysis / |c Elias M. Stein & Rami Shakarchi.
- 260 __ |a [北京 : |b 世界图书出版公司, |c 2013.]
- 300 __ |a xv, 423 p. : |b ill. ; |c 23 cm.
- 490 0_ |a Princeton lectures in analysis ; |v 4
- 500 __ |a Chinese title on cover.
- 504 __ |a Includes bibliographical references (p. 409-416) and index.
- 520 __ |a "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" --
- 520 __ |a "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"--
- 534 __ |p Reprint. Originally published: |c Princeton : Princeton University Press, c2011. |z 9780691113876.
- 650 _0 |a Functional analysis.
- 700 1_ |a Shakarchi, Rami.
- 950 __ |a SCNU |f O177/S819