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Frames from Functional Calculus
Ilya Krishtal, Javad Mashreghi, Brendan Miller
We introduce frames generated by applying families of functions to a diagonal operator through functional calculus, with diagonal entries forming a Carleson interpolating sequence.…
Block Diagonal Carleson Frames
Ilya Krishtal, Brendan Miller
We introduce \textit{block diagonal Carleson frames}, i.e. singly generated dynamical frames in which the generating operator is block diagonal. We classify all such frames when th…
Demystifying Carleson Frames
Ilya Krishtal, Brendan Miller
We study spanning properties of Carleson systems and prove a recent conjecture on frame subsequences of Carleson frames. In particular, we show that if is…
The normalized orbit of a bounded normal operator can be a frame
Ilya A. Krishtal, Götz E. Pfander
Conjecture 3 in [A. Aldroubi, C. Cabrelli, I. Krishtal, and U. Molter, Dynamical Sampling: A Survey, La Matematica 5 (2026), Article 37] postulates that for any bounded normal oper…
Dynamical Sampling: A Survey
Akram Aldroubi, Carlos Cabrelli, Ilya Krishtal +1
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…