Smooth Analysis in Banach Spaces 1st Edition by Petr Hájek, Michal Johanis 9783110258981 3110258986
Original price was: $50.00.$35.00Current price is: $35.00.
Smooth Analysis in Banach Spaces 1st Edition by Petr Hájek, Michal Johanis – Ebook PDF Instant Download/Delivery: 9783110258981, 3110258986
Full download Smooth Analysis in Banach Spaces 1st Edition after payment
Product details:
ISBN 10: 3110258986
ISBN 13: 9783110258981
Author: Petr Hájek, Michal Johanis
This book is about the 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 infinite dimension where measure and compactness are not available? The subject of infinite dimensional real higher smoothness is treated here for the first time in full detail, therefore this book may also serve as a reference book.
Table of contents:
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 Lp-norms on ℝn
5. Polynomial identities
6. Estimates of coefficients of polynomials
7. Notes and remarks
Chapter 3 – Weak continuity of polynomials and estimates of coefficients
1. Tensor products and spaces of multilinear mappings
2. Weak continuity and spaces of polynomials
3. Weak continuity and ℓ1
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
6. Sub-symmetric polynomials on ℝn
7. 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. Lp 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
4. Uniformly smooth mappings from C(K), K scattered
5. Uniformly smooth mappings from -spaces
6. Fixing the canonical basis of c0
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 c0(Γ)
7. Approximation of Lipschitz mappings
8. Approximation of C1-smooth mappings
9. Approximation of norms
10. Notes and remarks
People also search:
smooth analysis in banach spaces
analysis in banach spaces
what is banach space in functional analysis
banach spaces for analysts
an introduction to banach space theory pdf
Tags: Petr Hájek, Michal Johanis, Smooth, Banach