Journal of Operator Theory

Volume 51, Issue 1, Winter 2004 pp. 35-48.

Analytic finite band width reproducing kernels and operator weighted shifts

Authors: G.T. Adams, (1) P.J. McGuire, (2) N. Salinas, (3) and A.R. Schweinsberg (4)
Author institution: (1) Mathematics Department, Bucknell University, Lewisburg, PA 17837, USA
(2) Department of Mathematics, University of Kansas, Lawrence, Kansas 66045-2142, USA
(3) Department of Mathematics, University of Kansas, Lawrence, Kansas 66045-2142, USA
(4) Mathematics Department, Bucknell University, Lewisburg, PA 17837, USA

Summary: This paper realizes the reproducing kernel Hilbert spaces with orthonormal bases of the form $\{ (a_{{}_{n,0}} +a_{{}_{n,1}}z +\cdots + a_{{}_{n,J}} z^{J}) z^n : n \geq 0 \}$ in a matrix valued kernel setting. The question of when multiplication by $\phi$, denoted $M_\phi$, is a bounded operator is investigated and it is shown that $M_\phi$ can be viewed as the compression of a matrix valued Toeplitz type operator.

Keywords: Reproducing kernels, multiplication operators, orthogonal polynomials, operator weighted shifts

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