Frames induced by the action of continuous powers of an operator

Aldroubi, A.; Huang, L. X.; Petrosyan, A.

doi:10.1016/j.jmaa.2019.05.066

Title: Frames induced by the action of continuous powers of an operator

Journal Article · 05 June 2019 · Journal of Mathematical Analysis and Applications

DOI: https://doi.org/10.1016/j.jmaa.2019.05.066 · OSTI ID:1559576

Aldroubi, A. ^[1]; Huang, L. X. ^[1]; Petrosyan, A. ^[2]

Vanderbilt Univ., Nashville, TN (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

We investigate systems of the form {A^tg : g ϵ $$\mathcal{G}$$, t ϵ [0, L]} where A ϵ $$\mathcal{B}$$($$\mathcal{H}$$) is a normal operator in a separable Hilbert space $$\mathcal{H}$$, $$\mathcal{G}$$ c $$\mathcal{H}$$ is a countable set, and L is a positive real number. While the main goal of this work is to study the frame properties of {A^tg : g ϵ $$\mathcal{G}$$, t ϵ [0, L]}, as intermediate steps, we investigate the completeness and Bessel properties of such systems from a theoretical perspective, which are of interest by themselves. Beside the theoretical appeal of investigating such systems, their connections to dynamical and mobile sampling make them fundamental for understanding and solving several major problems in engineering and science.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1559576

Journal Information:: Journal of Mathematical Analysis and Applications, Vol. 478, Issue 2; ISSN 0022-247X

Country of Publication:: United States

Language:: English

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Cited by: 8 works

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Frames induced by continuous powers of operators

Title: Frames induced by the action of continuous powers of an operator

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