Three problems on exponential bases
Laura De Carli, Alberto Mizrahi, Alexander Tepper
TL;DR
This paper investigates conditions under which exponential bases serve as frames, Riesz sequences, or Riesz bases in L^2 spaces over specific sets D in R^d, focusing on three key cases.
Contribution
It analyzes three special cases of the problem of characterizing exponential bases as frames or Riesz bases on sets D with finite measure.
Findings
Identifies conditions for exponential bases to form frames on D.
Determines when exponential bases are Riesz sequences on D.
Establishes criteria for exponential bases to be Riesz bases on D.
Abstract
We consider three special and significant cases of the following problem. Let D be a (possibly unbounded) set of finite Lebesgue measure in R^d. Find conditions on D for which the standard exponential basis on the unit cube of R^d is a frame, a Riesz sequence, or a Riesz basis on L^2(D).
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