Analysis Seminar

SPEAKER: Mr. James Sunkes

TITLE: The Fiber Dimension of Analytic Operators

ABSTRACT: In this talk, I will discuss the fiber dimension of an invariant subspace of an analytic operator. The main goal of the seminar is to prove a formula which shows that the fiber dimension is a limit which involves the dimension of the projections onto the orthogonal

complements of T^{k}H. The results proven are largely be based on the work on Fang (from 2005). If time permits, we will show a connection between the Fiber Dimension and an algebraic quantity known as the Samuel multiplicity.