Exponential bases, Paley-Wiener spaces and applications
Alex Iosevich, Azita Mayeli
TL;DR
This paper explores the relationship between translation bases in Paley-Wiener spaces and exponential Fourier bases, applying these insights to characterize vector-valued time-frequency translates of signals.
Contribution
It establishes a novel connection between translation bases and exponential Fourier bases within Paley-Wiener spaces, with applications to time-frequency analysis.
Findings
Characterization of translation bases in Paley-Wiener spaces
Connection between translation bases and exponential Fourier bases
Application to vector-valued time-frequency translates
Abstract
We investigate the connection between translation bases for Paley-Wiener spaces and exponential Fourier bases for a domain. We apply these results to the characterization of vector-valued time-frequency translates of a Paley-Wiener "window" signal.
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