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Smooth analysis in Banach spaces /
This bookis aboutthe subject of higher smoothness in separable real Banach spaces. It brings together several angles of view on polynomials, both in finite and infinite setting. Also a rather thorough and systematic view of the more recent results, and the authors work is given. The book revolves ar...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin ; München ; Boston :
DE GRUYTER,
2014.
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| Edición: | 2014. |
| Colección: | De Gruyter series in nonlinear analysis and applications.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
|---|---|---|---|
| 001 | EBOOKCENTRAL_ocn897443938 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
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| 020 | |z 3110258986 | ||
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| 035 | |a (OCoLC)897443938 |z (OCoLC)897564754 |z (OCoLC)898769617 |z (OCoLC)958353919 | ||
| 050 | 4 | |a QA322.2 .H35 2014 | |
| 072 | 7 | |a QA |2 lcco | |
| 082 | 0 | 4 | |a 510 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Hájek, Petr. | |
| 245 | 1 | 0 | |a Smooth analysis in Banach spaces / |c Petr Hájek, Michal Johanis. |
| 250 | |a 2014. | ||
| 264 | 1 | |a Berlin ; |a München ; |a Boston : |b DE GRUYTER, |c 2014. | |
| 300 | |a 1 online resource | ||
| 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 De Gruyter Series in Nonlinear Analysis and Applications ; |v v. 19 | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Introduction; Chapter 1. Fundamental properties of smoothness; 1. Multilinear mappings and polynomials; 2. Complexification; 3. Fréchet smoothness; 4. Taylor polynomial; 5. Smoothness classes; 6. Power series and their convergence; 7. Complex mappings; 8. Analytic mappings; 9. Notes and remarks; Chapter 2. Basic properties of polynomials on Rn; 1. Spaces of polynomials on Rn; 2. Cubature formulae; 3. Estimates related to Chebyshev polynomials; 4. Polynomials and L_p-norms on Rn; 5. Polynomial identities; 6. Estimates of coefficients of polynomials; 7. Notes and remarks. | |
| 505 | 8 | |a Chapter 3. Weak continuity of polynomials and estimates of coefficients1. Tensor products and spaces of multilinear mappings; 2. Weak continuity and spaces of polynomials; 3. Weak continuity and _1; 4. (p, q)-summing operators; 5. Estimates of coefficients of multilinear mappings; 6. Bohr radius; 7. Notes and remarks; Chapter 4. Asymptotic properties of polynomials; 1. Finite representability and ultraproducts; 2. Spreading models; 3. Polynomials and p-estimates; 4. Separating polynomials. Symmetric and sub-symmetric polynomials; 5. Stabilisation of polynomials. | |
| 505 | 8 | |a 6. Sub-symmetric polynomials on Rn7. Polynomial algebras on Banach spaces; 8. Notes and remarks; Chapter 5. Smoothness and structure; 1. Convex functions; 2. Smooth bumps and structure I; 3. Smooth variational principles; 4. Smooth bumps and structure II; 5. Local dependence on finitely many coordinates; 6. Isomorphically polyhedral spaces; 7. L_p spaces; 8. C(K) spaces; 9. Orlicz spaces; 10. Notes and remarks; Chapter 6. Structural behaviour of smooth mappings; 1. Weak uniform continuity and higher smoothness; 2. Bidual extensions; 3. Class ==========W. | |
| 505 | 8 | |a 4. Uniformly smooth mappings from C(K), K scattered5. Uniformly smooth mappings from ==========W-spaces; 6. Fixing the canonical basis of c_0; 7. Ranges of smooth mappings; 8. Harmonic behaviour of smooth mappings; 9. Notes and remarks; Chapter 7. Smooth approximation; 1. Separation; 2. Approximation by polynomials; 3. Approximation by real-analytic mappings; 4. Infimal convolution; 5. Approximation of continuous mappings and partitions of unity; 6. Non-linear embeddings into c_0(); 7. Approximation of Lipschitz mappings; 8. Approximation of C1-smooth mappings; 9. Approximation of norms. | |
| 505 | 8 | |a 10. Notes and remarksBibliography; Notation; Index. | |
| 520 | |a This bookis aboutthe subject of higher smoothness in separable real Banach spaces. It brings together several angles of view on polynomials, both in finite and infinite setting. Also a rather thorough and systematic view of the more recent results, and the authors work is given. The book revolves around two main broad questions: What is the best smoothness of a given Banach space, and its structural consequences? How large is a supply of smooth functions in the sense of approximating continuous functions in the uniform topology, i.e. how does the Stone-Weierstrass theorem generalize into in. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Banach spaces. | |
| 650 | 0 | |a Normed linear spaces. | |
| 650 | 0 | |a Polynomials. | |
| 650 | 6 | |a Espaces de Banach. | |
| 650 | 6 | |a Espaces linéaires normés. | |
| 650 | 6 | |a Polynômes. | |
| 650 | 7 | |a Banach spaces |2 fast | |
| 650 | 7 | |a Normed linear spaces |2 fast | |
| 650 | 7 | |a Polynomials |2 fast | |
| 650 | 7 | |a Polynom |2 gnd | |
| 650 | 7 | |a Banach-Raum |2 gnd | |
| 650 | 7 | |a Stetige Abbildung |2 gnd | |
| 650 | 7 | |a Glatte Funktion |2 gnd | |
| 700 | 1 | |a Johanis, Michal. | |
| 776 | 0 | |c Print |z 9783110258981 | |
| 830 | 0 | |a De Gruyter series in nonlinear analysis and applications. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=1130389 |z Texto completo |
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