The normalized orbit of a bounded normal operator can be a frame, providing a counterexample to Conjecture 3.
Dynamical Sampling: A Survey
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abstract
Dynamical sampling refers to a class of problems in which space-time samples are taken from a signal evolving under an underlying dynamical system. The goal is to use these samples to recover relevant information about the system, such as the initial state, the evolution operator, or the sources and sinks driving the dynamics. These problems are tightly connected to frame theory, operator theory, functional analysis, and other foundational areas of mathematics; they also give rise to new theoretical questions and have applications across engineering and the sciences. This survey provides an overview of the theoretical underpinnings of dynamical sampling, summarizes recent results, and outlines directions for future work, including open problems and conjectures.
fields
math.FA 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
New frame constructions from operator orbits generalize earlier results and disprove a conjecture on Carleson frames in Hilbert spaces.
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The normalized orbit of a bounded normal operator can be a frame
The normalized orbit of a bounded normal operator can be a frame, providing a counterexample to Conjecture 3.
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Frame constructions associated with operator orbits
New frame constructions from operator orbits generalize earlier results and disprove a conjecture on Carleson frames in Hilbert spaces.