Iterative Action of Normal Operators

ALDROUBI, AKRAM; CABRELLI, CARLOS A.; AHMET FARUK CAKMAK; MOLTER, URSULA; PETRSYAN, ARMENAK

JOURNAL OF FUNCTIONAL ANALYSIS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2017 vol. 272 p. 1121 - 1146

0022-1236

Let $A$ be a normal operator in a Hilbert space $HH$, and let $G subset HH$ be a countable set of vectors. We investigate the relations between $A$, $G$ and $L$ that make the system of iterations ${A^ng: gin G,;0leq n< L(g)}$ complete, Bessel, a basis, or a frame for $HH$. 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.