Iterative actions of normal operators

By Akram Aldroubi, Carlos Cabrelli, A. Cakmak, Ursula Molter, Armenak Petrosyan. 2016

99 citations recorded by the source corpus.

Let $A$ be a normal operator in a Hilbert space $\mathcal{H}$, and let $\mathcal{G} \subset \mathcal{H}$ be a countable set of vectors. We investigate the relations between $A$, $\mathcal{G}$ , and $L$ that makes the system of iterations $\{A^ng: g\in \mathcal{G},\;0\leq n< L(g)\}$ complete, Bessel, a basis, or a frame for $\mathcal{H}$. The problem is motivated by the dynamical sampling problem and is connected to several topics in functional analysis, including, frame theory and spectral theory. It also has relations to topics in applied harmonic analysis including, wavelet theory and time-frequency analysis.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7e6581059a30f6f318dc7410af8310e06ad04ec0

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In Applied Mathematics

In Computer Vision and Pattern Recognition

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Citations in the corpus

Frame properties of operator orbits (2018, background): “Dynamical sampling has already attracted considerable attention [1, 2, 4, 5, 6, 8, 9, 10, 11, 12, 20].”
Frame properties of systems arising via iterated actions of operators (2019, result): “This result justifies some of the no-go results in the papers [2, 1, 3], typically of the form that certain conditions on the involved operators (including boundedness) would imply that the iterated system can not be a frame.”
Dynamical sampling and frame representations with bounded operators (2018, background): “Further references to dynamical sampling include [2, 3, 4, 5, 13, 1, 7, 8].”
Dynamical Sampling and Systems from Iterative Actions of Operators (2016, methodology): “;2;:::;¥gis a m measurable function. Dynamical sampling and systems from iterative actions of operators 7 2.3 Action of normal operators via inﬁnite iterations In this section we present results from [3] about a system of inﬁnite iterative action fAng ig i2I;n0 of a given normal operator A 2B(H ) on”