Operator-Valued frame generators for group-like unitary systems
Bin Meng
TL;DR
This paper explores operator-valued frames within group-like unitary systems, characterizing their commutants and conditions for Parseval duals, advancing the mathematical understanding of structured frame systems.
Contribution
It introduces a characterization of the commutant of group-like unitary systems and provides conditions for operator-valued frame generators to admit Parseval duals.
Findings
Characterization of the commutant via analysis operators
Necessary and sufficient conditions for Parseval duals
Enhanced understanding of operator-valued frames in structured systems
Abstract
In this paper, we investigate operator-valued frames with the structure of group-like unitary system. We show the commutant of the group-like unitary system can be characterized in terms of analysis operators associated with all the operator-valued Bessel generators and give some sufficient and necessary conditions to describe when an operator-valued frame generator admits a Parseval dual.
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Taxonomy
TopicsMathematical Analysis and Transform Methods