Abstract
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.
Keywords
Hilbert space
Countable set
Mathematics
Bessel function
Basis (linear algebra)
Operator (biology)
Operator theory
Frame (networking)
Discrete mathematics
Pure mathematics
Combinatorics
Mathematical analysis
Computer science
Subject Areas
Mathematical Analysis and Transform Methods
·Applied Mathematics ·Physical Sciences
Image and Signal Denoising Methods
·Computer Vision and Pattern Recognition ·Physical Sciences
Medical Imaging Techniques and Applications
·Radiology, Nuclear Medicine and Imaging ·Health Sciences
Citations by Year
2017: 1
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