Differentiation in real topological vector spaces

Speaker: Bryce Virgin

Date/Time: Friday, April 15th, at 2:00pm

Abstract: Differentiation is a fundamental operation in the subject of analysis, which systematizes the process of approximating sufficiently regular functions and shapes with linear substitutes near points of interest. Many of the classical results of analysis deal with the properties of differentiation for maps between finite dimensional, Euclidean vector spaces, where the theory of differentiation is well-behaved. There is little difficulty in extending the concept of differentiation to quite general topological vector spaces, but in this case, derivatives will no longer act as expected. The talk will explore the generalization of the standard derivative to general real topological vector spaces, which important theorems and properties it retains from the Euclidean case, and which are lost in the generalization.

Видео Differentiation in real topological vector spaces канала USF GradMath