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 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 dif...