Multivariable versions of Kaluza's Lemma

Speaker: Stefan Richter (University of Tennessee, Knoxville TN)

Abstract: Let d be a positive integer and let f be an analytic function in a neighborhood of the origin in complex d-space. We present two independent conditions on the positive Taylor coefficients of f, each of which implies that f(z)=1/(1-g(z))  for a function g with non-negative Taylor coefficients. The results have applications in the theory of Nevanlinna-Pick kernels.