Principal functions for bi-free central limit distributions

Abstract

We find the principal function of the completely non-normal operator l(v_1)+l(v_1)^*+i(r(v_2)+r(v_2)^*) on a subspace of the full Fock space F(H) which arises from a bi-free central limit distribution. As an application, we find the essential spectrum of this operator.

13 pages, including 1 figure

References in corpus (2)

• Free Probability for Pairs of Faces I
• Free Probability for Pairs of Faces II: 2-Variables Bi-free $R$-Transform and Systems with Rank $\le 1$ Commutation