Journal of Operator Theory

Volume 43, Issue 1, Winter 2000 pp. 43-68.

Completely and alternatingly hyperexpansive operators

Authors: V.M. Sholapurkar (1), and Ameer Athavale (2)
Author institution: (1) Department of Mathematics, University of Pune, Pune - 411007, India
(2) Department of Mathematics, University of Pune, Pune - 411007, India

Summary: Special classes of functions on the classical semigroup

${\bbb N}$ of non-negative integers, arising through the mechanism of difference operators, can be associated in a natural way with special classes of bounded linear operators on Hilbert spaces. The interplay among the theories of special classes of functions on

${\bbb N}$ gets mirrored in the interaction among the associated classes of operators and leads to a fruitful synthesis of the theory of harmonic analysis on semigroups with operator theory. The present paper is a specific illustration of that theme.

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