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Functional analysis : introduction to further topics in analysis /
"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 theo...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton, N.J. :
Princeton University Press,
2011.
|
| Colección: | Princeton lectures in analysis ;
4. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 003 | OCoLC | ||
| 005 | 20231005004200.0 | ||
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| 008 | 110921s2011 nju ob 001 0 eng d | ||
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| 100 | 1 | |a Stein, Elias M., |d 1931-2018, |e author. | |
| 245 | 1 | 0 | |a Functional analysis : |b introduction to further topics in analysis / |c Elias M. Stein, Rami Shakarchi. |
| 260 | |a Princeton, N.J. : |b Princeton University Press, |c 2011. | ||
| 300 | |a 1 online resource (xv, 423 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Princeton lectures in analysis ; |v 4 | |
| 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 "-- |c Provided by publisher | ||
| 520 | |a "This book covers such topics as L^p 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"-- |c Provided by publisher | ||
| 504 | |a Includes bibliographical references (pages 413-416) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover; Contents; Foreword; Preface; Chapter 1. L[sup(p)] Spaces and Banach Spaces; 1 L[sup(p)] spaces; 1.1 The Hölder and Minkowski inequalities; 1.2 Completeness of L[sup(p)]; 1.3 Further remarks; 2 The case p = ∞; 3 Banach spaces; 3.1 Examples; 3.2 Linear functionals and the dual of a Banach space; 4 The dual space of L[sup(p)] when 1 ≤ p < ∞; 5 More about linear functionals; 5.1 Separation of convex sets; 5.2 The Hahn-Banach Theorem; 5.3 Some consequences; 5.4 The problem of measure; 6 Complex L[sup(p)] and Banach spaces; 7 Appendix: The dual of C(X) | |
| 505 | 8 | |a 7.1 The case of positive linear functionals7.2 The main result; 7.3 An extension; 8 Exercises; 9 Problems; Chapter 2. L[sup(p)] Spaces in Harmonic Analysis; 1 Early Motivations; 2 The Riesz interpolation theorem; 2.1 Some examples; 3 The L[sup(p) theory of the Hilbert transform; 3.1 The L[sup(2)] formalism; 3.2 The L[sup(p) theorem; 3.3 Proof of Theorem 3.2; 4 The maximal function and weak-type estimates; 4.1 The L[sup(p)] inequality; 5 The Hardy space H[sup(1)][sub(r); 5.1 Atomic decomposition of H[sup(1)[sub(r); 5.2 An alternative definition of H[sup(1)[sub(r)] | |
| 505 | 8 | |a 5.3 Application to the Hilbert transform6 The space H[sup(1)[sub(r)] and maximal functions; 6.1 The space BMO; 7 Exercises; 8 Problems; Chapter 3. Distributions: Generalized Functions; 1 Elementary properties; 1.1 Definitions; 1.2 Operations on distributions; 1.3 Supports of distributions; 1.4 Tempered distributions; 1.5 Fourier transform; 1.6 Distributions with point supports; 2 Important examples of distributions; 2.1 The Hilbert transform and pv(1/x); 2.2 Homogeneous distributions; 2.3 Fundamental solutions | |
| 505 | 8 | |a 2.4 Fundamental solution to general partial differential equations with constant coefficients2.5 Parametrices and regularity for elliptic equations; 3 Caldeórn-Zygmund distributions and L[sup(p)] estimates; 3.1 Defining properties; 3.2 The L[sup(p) theory; 4 Exercises; 5 Problems; Chapter 4. Applications of the Baire Category Theorem; 1 The Baire category theorem; 1.1 Continuity of the limit of a sequence of continuous functions; 1.2 Continuous functions that are nowhere differentiable; 2 The uniform boundedness principle; 2.1 Divergence of Fourier series; 3 The open mapping theorem | |
| 505 | 8 | |a 3.1 Decay of Fourier coefficients of L[sup(1)]-functions4 The closed graph theorem; 4.1 Grothendieck's theorem on closed subspaces of L[sup(p)]; 5 Besicovitch sets; 6 Exercises; 7 Problems; Chapter 5. Rudiments of Probability Theory; 1 Bernoulli trials; 1.1 Coin flips; 1.2 The case N = ∞; 1.3 Behavior of S[sub(N)] as N → ∞, first resultes; 1.4 Central limit theorem; 1.5 Statement and proof of the theorem; 1.6 Random series; 1.7 Random Fourier series; 1.8 Bernoulli trials; 2 Sums of independent random variables; 2.1 Law of large numbers and ergodic theorem; 2.2 The role of martingales | |
| 546 | |a English. | ||
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
| 590 | |a JSTOR |b Books at JSTOR All Purchased | ||
| 590 | |a JSTOR |b Books at JSTOR Evidence Based Acquisitions | ||
| 650 | 0 | |a Functional analysis. | |
| 650 | 6 | |a Analyse fonctionnelle. | |
| 650 | 7 | |a MATHEMATICS |x Functional Analysis. |2 bisacsh | |
| 650 | 7 | |a Functional analysis. |2 fast |0 (OCoLC)fst00936061 | |
| 700 | 1 | |a Shakarchi, Rami, |e author. | |
| 776 | 0 | 8 | |i Print version: |a Stein, Elias M., 1931- |t Functional analysis. |d Princeton, N.J. : Princeton University Press, 2011 |z 9780691113876 |w (DLC) 2011020971 |w (OCoLC)731009495 |
| 830 | 0 | |a Princeton lectures in analysis ; |v 4. | |
| 856 | 4 | 0 | |u https://jstor.uam.elogim.com/stable/10.2307/j.ctvcm4hpw |z Texto completo |
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| 994 | |a 92 |b IZTAP | ||