An analytic model for left invertible weighted translation semigroups

Phatak Geetanjali M. and Sholapurkar V. M.: An analytic model for left invertible weighted translation semigroups. In: Acta scientiarum mathematicarum, (85) 1-2. pp. 295-311. (2019)

[thumbnail of math_085_numb_001-002_295-311.pdf] Cikk, tanulmány, mű
math_085_numb_001-002_295-311.pdf
Restricted to: SZTE network

Download (231kB)

Abstract

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 L 2 (R+) by using a weight function. The operator St can be thought of as a continuous analogue of a weighted shift operator. In this paper, we show that every left invertible operator St can be modeled as a multiplication by z on a reproducing kernel Hilbert space H of vector-valued analytic functions on a certain disc centered at the origin and the reproducing kernel associated with H is a diagonal operator. As it turns out that every hyperexpansive weighted translation semigroup is left invertible, the model applies to these semigroups. We also describe the spectral picture for the left invertible weighted translation semigroup. In the process, we point out the similarities and differences between a weighted shift operator and an operator St.

Item Type: Article
Journal or Publication Title: Acta scientiarum mathematicarum
Date: 2019
Volume: 85
Number: 1-2
ISSN: 2064-8316
Page Range: pp. 295-311
Official URL: http://www.acta.hu
Related URLs: http://acta.bibl.u-szeged.hu/62105/
DOI: 10.14232/actasm-018-546-3
Uncontrolled Keywords: Matematika
Additional Information: Bibliogr.: p. 310-311. ; összefoglalás angol nyelven
Date Deposited: 2019. Sep. 25. 10:53
Last Modified: 2021. Mar. 25. 15:30
URI: http://acta.bibl.u-szeged.hu/id/eprint/62148

Actions (login required)

View Item View Item