2018/03/23 by Geetanjali M. Phatak, Phatak, Geetanjali M., V. M. Sholapurkar +1 · 1 citation
Mathematics · #Holomorphic and Operator Theory #Advanced Topics in Algebra #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1803.08623
The weighted shift operators turn out to be extremely useful in supplying interesting examples of operators on Hilbert spaces. With a view to study a continuous analogue of weighted shifts, M. Embry and A. Lambert initiated the study of a semigroup of operators \St\ indexed by a non-negative real number t and termed it as weighted translation semigroup. The operators St are defined on L2(\mathbb R+) by using a weight function. In this paper, we continue the work carried out there and obtain characterizations of hyperexpansive weighted translation semigroups in terms of their symbols. We also discuss Cauchy dual of a hyperexpansive weighted translation semigroup. As an application of the techniques developed, we present new proofs of a couple of known results.