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Banach, Fréchet, Hilbert and Neumann spaces /
This book is the first of a set dedicated to the mathematical tools used in partial differential equations derived from physics. Its focus is on normed or semi-normed vector spaces, including the spaces of Banach, Fréchet and Hilbert, with new developments on Neumann spaces, but also on extractable...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London :
John Wiley & Sons, Incorporated,
2016.
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| Colección: | Analysis for PDEs set ;
volume 1. Mathematics and statistics series (ISTE) |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Introduction
- Familiarization with semi-normed spaces
- Notations
- Prerequisites
- Part 1. Semi-normed spaces ; Semi-normed spaces
- Comparison of semi-normed spaces
- Banach, Fréchet and Neumann spaces
- Hilbert spaces
- Product, intersection, sum and quotient of spaces
- Part 2. Continuous mappings ; Continuous mappings
- Images of sets under continuous mappings
- Properties of mappings in metrizable spaces
- Extension of mappings, equicontinuity
- Compactness in mapping spaces
- Spaces of linear or multilinear mappings
- Part 3. Weak topologies ; Duality
- Dual of a subspace
- Weak topology
- Properties of sets for the weak topology
- Reflexivity
- Extractable spaces
- Part 4. Differential calculus ; Differentiable mappings
- Differentiation of multivariable mappings
- Successive differentiations
- Derivation of functions of one real variable.