ANALYTIC FINITE BAND WIDTH REPRODUCING KERNELS
AND OPERATOR WEIGHTED SHIFTS
GREGORY T. ADAMS, PAUL J. MCGUIRE, NORBERTO SALINAS, AND ALLEN R.
SCHWEINSBERG
Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837, USA
This paper realizes 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}
in a matrix valued kernel setting. The question of when multiplication by
z,
denoted M_z, is a bounded operator is investigated and it is shown that M_z
can be viewed as the compression of a matrix valued Toeplitz type operator.