Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-28T03:32:36.272Z Has data issue: false hasContentIssue false
  • English
  • Français

ANALYTIC TRIDIAGONAL REPRODUCING KERNELS

Published online by Cambridge University Press:  30 January 2002

GREGORY T. ADAMS  and
PAUL J. MCGUIRE
GREGORY T. ADAMS
Affiliation:
Mathematics Department, Bucknell University, Lewisburg, PA 17837, USA; [email protected], [email protected]
PAUL J. MCGUIRE
Affiliation:
Mathematics Department, Bucknell University, Lewisburg, PA 17837, USA; [email protected], [email protected]
Get access

Abstract

The paper characterizes the reproducing kernel Hilbert spaces with orthonormal bases of the form {(an,0+an,1z+…+an,JzJ)zn, 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 Mz on a tridiagonal space is strikingly different from that on any diagonal space.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 64 , Issue 3 , December 2001 , pp. 722 - 738
Copyright
London Mathematical Society 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)