Analysis Seminar: "Monomial Operators"

Speaker: John McCarthy, Washington University in Saint Louis

Abstract: An operator T on L^2[0,1] is called a monomial operator if there exists some number N and a sequence c_n so that
                T(x^n) = c_n x^(n+N)
for every natural number n. Examples include the Volterra operator, multiplication by x, and the Hardy operator.

I shall show that every monomial operator leaves invariant every space of the form {f = 0 on [0,s]}. The proof relies on an asymptotic version of the Muntz-Szasz theorem.

This is joint work with Jim Agler.

Host: John McCarthy