Jacques Simon – författare

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.

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.

This book is the second of a set dedicated to the mathematical tools used in partial differential equations derived from physics. It presents the properties of continuous functions, which are useful for solving partial differential equations, and, more particularly, for constructing distributions valued in a Neumann space. The author examines partial derivatives, the construction of primitives, integration and the weighting of value functions in a Neumann space. Many of them are new generalizations of classical properties for values in a Banach space. 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.

This book is the second of a set dedicated to the mathematical tools used in partial differential equations derived from physics. It presents the properties of continuous functions, which are useful for solving partial differential equations, and, more particularly, for constructing distributions valued in a Neumann space. The author examines partial derivatives, the construction of primitives, integration and the weighting of value functions in a Neumann space. Many of them are new generalizations of classical properties for values in a Banach space. 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.