Abstract

This paper characterizes the reproducing kernel Hilbert spaces
with orthonormal bases of the form ${(a_{n;0} + a_{n;1} z + ... + a_{n;J} z^J ) z^n; n >= 0}$.
The primary focus is on the tridiagonal case where $J = 1$ and how it compares
to 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 $M_z$ 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.

Paper

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