Nonlinear Functional Analysis
by Gerald Teschl
Publisher: University of Vienna 2009
Number of pages: 74
This manuscript provides a brief introduction to nonlinear functional analysis. We start out with calculus in Banach spaces, review differentiation and integration, derive the implicit function theorem and apply the result to prove existence and uniqueness of solutions for ordinary differential equations in Banach spaces. Next we introduce the mapping degree in both finite and infinite dimensional Banach spaces.
Home page url
Download or read it online for free here:
by Alexander C. R. Belton - Lancaster University
These lecture notes are an expanded version of a set written for a course given to final-year undergraduates at the University of Oxford. A thorough understanding of Banach and Hilbert spaces is a prerequisite for this material.
by Javier Bernal - arXiv.org
As shape analysis is intricately related to Lebesgue integration and absolute continuity, it is advantageous to have a good grasp of the two notions. We review basic concepts and results about Lebesgue integration and absolute continuity.
by Gerald Teschl - Universitaet Wien
This manuscript provides a brief introduction to Real and (linear and nonlinear) Functional Analysis. It covers basic Hilbert and Banach space theory as well as basic measure theory including Lebesgue spaces and the Fourier transform.
by Ville Turunen - Aalto TKK
In this book you will learn something about functional analytic framework of topology. And you will get an access to more advanced literature on non-commutative geometry, a quite recent topic in mathematics and mathematical physics.