Riesz bases of exponentials on unbounded multi-tiles
Copyright policy )Riesz bases of exponentials on unbounded multi-tiles
We prove the existence of Riesz bases of exponentials of L 2 ( Ω ) L^2(\Omega ) , provided that Ω ⊂ R d \Omega \subset \mathbb {R}^d is a measurable set of finite and positive measure, not necessarily bounded, that satisfies a multi-tiling condition and an arithmetic property that we call admissibility. This property is satisfied for any bounded domain, so our results extend the known case of bounded multi-tiles. We also extend known results for submulti-tiles and frames of exponentials to the unbounded case.
- National Scientific and Technical Research Council Argentina
- University of Buenos Aires Argentina
Paley-Wiener spaces, Trigonometric approximation, Trigonometric interpolation, FRAMES OF EXPONENTIALS, MULTI-TILING, General harmonic expansions, frames, SUBMULTI- TILING, frames of exponentials, shift-invariant spaces, RIESZ BASES OF EXPONENTIALS, multi-tiling, Mathematics - Classical Analysis and ODEs, Riesz bases of exponentials, SHIFT-INVARIANT SPACES, Tilings in \(n\) dimensions (aspects of discrete geometry), Classical Analysis and ODEs (math.CA), FOS: Mathematics, https://purl.org/becyt/ford/1.1, submulti-tiling, 42B99, 42C15, https://purl.org/becyt/ford/1, PALEY-WIENER SPACES
Paley-Wiener spaces, Trigonometric approximation, Trigonometric interpolation, FRAMES OF EXPONENTIALS, MULTI-TILING, General harmonic expansions, frames, SUBMULTI- TILING, frames of exponentials, shift-invariant spaces, RIESZ BASES OF EXPONENTIALS, multi-tiling, Mathematics - Classical Analysis and ODEs, Riesz bases of exponentials, SHIFT-INVARIANT SPACES, Tilings in \(n\) dimensions (aspects of discrete geometry), Classical Analysis and ODEs (math.CA), FOS: Mathematics, https://purl.org/becyt/ford/1.1, submulti-tiling, 42B99, 42C15, https://purl.org/becyt/ford/1, PALEY-WIENER SPACES
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