Upper Beurling density of systems formed by translates of finite sets of elements in \(L^p(\mathbb{R}^d)\)

DOI10.15352/BJMA/1342210162zbMath1243.42044arXiv1203.6147OpenAlexW2151559030MaRDI QIDQ437725

Bei Liu, Rui Liu

Publication date: 18 July 2012

Published in: Banach Journal of Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.6147

zbMATH Keywords

\(L^p\)-spacetranslate\((C_q)\)-system\(p'\)-Bessel sequenceupper Beurling density

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Completeness of sets of functions in nontrigonometric harmonic analysis (42C30)

Related Items (5)

Schauder frames and completeness of translates in the Orlicz space ⋮ \((X_d,x_d^\ast)\)-Bessel multipliers in Banach spaces ⋮ Unconditional Schauder frames of translates in \(L_p ( \mathbb{R}^d)\) ⋮ Parseval \(p\)-frames and the Feichtinger conjecture ⋮ Beurling density on expansible locally compact groups and systems of translations

Cites Work

• Frame expansions in separable Banach spaces
• From exact systems to Riesz bases in the Balian-Low theorem
• Sparse exponential systems: completeness with estimates
• Quasi-frames of translates
• Completeness of integer translates in function spaces on \(\mathbb{R}\)
• The art of frame theory
• Density of Gabor frames
• \(p\)-frames in separable Banach spaces
• Frames containing a Riesz basis and approximation of the frame coefficients using finite-dimensional methods
• History and evolution of the density theorem for Gabor frames
• Systems formed by translates of one element in $L_{p}(\mathbb R)$
• Difference Equations Over Locally Compact Abelian Groups
• Completeness in L2(ℝ) of almost integer translates
• A Class of Nonharmonic Fourier Series
• An introduction to frames and Riesz bases
• \(p\)-frames and shift invariant subspaces of \(L^p\)
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