CMA Workshop on Spectral Theory

The physicist R. Feynman advanced an idea of forming an abstract operator calculus for a finite number of noncommuting operators by attaching time indices to the operators. In joint work with G.W. Johnson, time-ordering measures are introduced to serve as weights for various functional calculi, such as the Weyl functional calculus (equal weights), the Kohn-Nirenberg or ordered functional calculus (ordered supports) and Maslov’s functional calculus (mixed supports). With two operators, replacing one time-ordering measure by Brownian motion and taking the other to be Lebesgue measure, we obtain a representation of the solution of a linear stochastic differential equation in a Banach space. The talk reports on current work with Z. Brzezniak examining how far Feynman’s idea can be pushed for linear stochastic PDE in Banach spaces.