Journal article
Signed Representing Measures (Berger-Type Charges) in Subnormality and Related Properties of Weighted Shifts: Signed Representing Measures
Resultate der Mathematik, Vol.81(1), 17
12/15/2025
DOI: 10.1007/s00025-025-02574-4
Appears in UI Libraries Support Open Access
Abstract
In the study ([5]) of the geometrically regular weighted shifts (GRWS), signed representing measures, which we call Berger-type charges, played an important role. Motivated by their utility in that context, we establish a general theory for Berger-type charges. We give the first result of which we are aware showing that k–hyponormality alone, as opposed to subnormality, yields measure/charge-related information. More precisely, for signed countably atomic measures with a decreasing sequence of atoms, we prove that k-hyponormality of the associated shift forces positivity of the densities of the largest atoms. Further, for certain completely hyperexpansive weighed shifts, we exhibit a Berger-type charge representation, in contrast but related to the classical Lévy-Khinchin representation. We use Berger-type charges to investigate when a non-subnormal GRWS weighted shift may be scaled to become conditionally positive definite, and close with an example indicating a distinction between the study of moment sequences and the study of weighted shifts.
Details
- Title: Subtitle
- Signed Representing Measures (Berger-Type Charges) in Subnormality and Related Properties of Weighted Shifts: Signed Representing Measures
- Creators
- Chafiq Benhida - Université de LilleRaúl E. Curto - University of IowaGeorge R. Exner - Bucknell University
- Resource Type
- Journal article
- Publication Details
- Resultate der Mathematik, Vol.81(1), 17
- DOI
- 10.1007/s00025-025-02574-4
- ISSN
- 1422-6383
- eISSN
- 1420-9012
- Publisher
- Springer Nature
- Grant note
- DMS-2247167 / National Science Foundation (http://dx.doi.org/10.13039/100000001)
- Language
- English
- Date published
- 12/15/2025
- Academic Unit
- Mathematics
- Record Identifier
- 9985091805602771
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