General

Authors

Search


Committee login



 
 

 


 

 

Forthcoming

Small thumbnail

Dynamics of Large Structures and Inverse Problems

Mathematical and Mechanical Engineering Set Volume 5

Small thumbnail

Civil Engineering Structures According to the Eurocodes

Small thumbnail

Swelling Concrete in Dams and Hydraulic Structures

DSC 2017

Small thumbnail

Earthquake Occurrence

Short- and Long-term Models and their Validation

Small thumbnail

The Chemostat

Mathematical Theory of Microorganims Cultures

Small thumbnail

From Prognostics and Health Systems Management to Predictive Maintenance 2

Knowledge, Traceability and Decision

Small thumbnail

First Hitting Time Regression Models

Lifetime Data Analysis Based on Underlying Stochastic Processes

Small thumbnail

The Innovative Company

An Ill-defined Object

Small thumbnail

Reading and Writing Knowledge in Scientific Communities

Digital Humanities and Knowledge Construction

Small thumbnail

Going Past Limits To Growth

A Report to the Club of Rome EU-Chapter

Small thumbnail

Banach, Fréchet, Hilbert and Neumann Spaces

Analysis for PDEs Set Volume 1

Jacques Simon, CNRS, France

ISBN: 9781786300096

Publication Date: May 2017   Hardback   362 pp.

130.00 USD


Add to cart

eBooks


Ebook Ebook

Description

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 spaces.
The author presents the main properties of these spaces, which are useful for the construction of Lebesgue and Sobolev distributions with real or vector values and for solving partial differential equations. Differential calculus is also extended to semi-normed spaces.
Simple methods, semi-norms, sequential properties and others are discussed, making these tools accessible to the greatest number of students doctoral students, postgraduate students engineers and researchers without restricting or generalizing the results.

Contents

1. Prerequisites.
2. Semi-normed Spaces.
3. Comparison of Semi-normed Spaces.
4. Banach, Fréchet and Neumann Spaces.
5. Hilbert Spaces.
6. Product, Intersection, Sum and Quotient of Spaces.
7. Continuous Mappings.
8. Images of Sets Under Continuous Mappings.
9. Properties of Mappings in Metrizable Spaces.
10. Extension of Mappings, Equicontinuity.
11. Compactness in Mapping Spaces.
12. Spaces of Linear or Multilinear Mappings.
13. Duality.
14. Dual of a Subspace.
15. Weak Topology.
16. Properties of Sets for the Weak Topology.
17. Reflexivity.
18. Extractable Spaces.
19. Differentiable Mappings.
20. Differentiation of Multivariable Mappings.
21. Successive Differentiations.
22. Derivation of Functions of One Real Variable.

About the Authors

Jacques Simon is Emeritus Research Director at CNRS. His research focuses on Navier-Stokes equations, particularly in shape optimization and in the functional spaces they use.

Downloads

DownloadTable of Contents - PDF File - 176 Kb

































0.01536 s.