Journal article
Moment infinitely divisible weighted shifts
Complex analysis and operator theory, Vol.13(1), pp.241-255
10/29/2017
DOI: 10.1007/s11785-018-0771-z
Abstract
Complex Anal. Oper. Theory 13(2019), 241-255 We say that a weighted shift $W_\alpha$ with (positive) weight sequence $\alpha: \alpha_0, \alpha_1, \ldots$ is {\it moment infinitely divisible} (MID) if, for every $t > 0$, the shift with weight sequence $\alpha^t: \alpha_0^t, \alpha_1^t, \ldots$ is subnormal. \ Assume that $W_{\alpha}$ is a contraction, i.e., $0 < \alpha_i \le 1$ for all $i \ge 0$. \ We show that such a shift $W_\alpha$ is MID if and only if the sequence $\alpha$ is log completely alternating. \ This enables the recapture or improvement of some previous results proved rather differently. \ We derive in particular new conditions sufficient for subnormality of a weighted shift, and each example contains implicitly an example or family of infinitely divisible Hankel matrices, many of which appear to be new.
Details
- Title: Subtitle
- Moment infinitely divisible weighted shifts
- Creators
- Chafiq BenhidaRaul E CurtoGeorge R Exner
- Resource Type
- Journal article
- Publication Details
- Complex analysis and operator theory, Vol.13(1), pp.241-255
- DOI
- 10.1007/s11785-018-0771-z
- ISSN
- 1661-8262
- eISSN
- 1661-8262
- Grant note
- name: Labex CEMPI, award: ANR-11-LABX-0007-01; DOI: 10.13039/100000001, name: National Science Foundation, award: DMS-1302666; name: Labex CEMPI, award: ANR-11-LABX-0007-01
- Language
- English
- Date published
- 10/29/2017
- Academic Unit
- Mathematics
- Record Identifier
- 9983985829602771
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