ANALYTIC TRIDIAGONAL REPRODUCING KERNELS

Source abstract

The paper characterizes the reproducing kernel Hilbert spaces with orthonormal bases of the form {( a n ,0 + a n ,1 z +…+ a n,J z J ) z n , n [ges ] 0}. The primary focus is on the tridiagonal case where J = 1, and on how it compares with the diagonal case where J = 0. The question of when multiplication by z is a bounded operator is investigated, and aspects of this operator are discussed. In the diagonal case, Mz is a weighted unilateral shift. It is shown that in the tridiagonal case, this need not be so, and an example is given in which the commutant of M z on a tridiagonal space is strikingly different from that on any diagonal space.