Jack Arbunich : Stone's Theorem (part 2)

Posted by Trevor Leslie , part of the Graduate Analysis Seminar.

At

April 15, 2015, 2 p.m.

In

SEO 427

Abstract

With bounded self-adjoint operators the exponential of an operator makes sense via its Taylor series as the series converges in norm. This method is not possible if our operator is unbounded. Stone's Theorem states that if we have a strongly continuous one parameter unitary group, then there is a self-adjoint operator $A$ on our Hilbert Space such that the one parameter group is the exponential of the operator $A$.