Complete interpolating sequences for Fourier transforms supported by convex symmetric pol\-y\-gons

DOI10.1007/BF02384495zbMath1038.42011MaRDI QIDQ1428359

Alexander Rashkovskii, Yurij I. Lyubarskij

Publication date: 28 March 2004

Published in: Arkiv för Matematik (Search for Journal in Brave)

zbMATH Keywords

Paley-Wiener spacetwo-dimensional Fourier transformcomplete interpolating sequence

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Fourier series and coefficients in several variables (42B05) Entire functions of several complex variables (32A15) Zero sets of holomorphic functions of several complex variables (32A60) Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs (32E30)

Related Items (17)

Riesz bases of exponentials for convex polytopes with symmetric faces ⋮ On Riesz Bases of Exponentials for Convex Polytopes with Symmetric Faces ⋮ Universal sampling and interpolation in locally compact abelian groups ⋮ On multi-dimensional sampling and interpolation ⋮ Nonuniform sampling and recovery of bandlimited functions in higher dimensions ⋮ Multi-tiling sets, Riesz bases, and sampling near the critical density in LCA groups ⋮ On minimal trajectories for mobile sampling of bandlimited fields ⋮ Exponential bases for partitions of intervals ⋮ Riesz bases, Meyer’s quasicrystals, and bounded remainder sets ⋮ Multi-tiling and Riesz bases ⋮ Sampling of entire functions of several complex variables on a lattice and multivariate Gabor frames ⋮ Recovery of bivariate band-limited functions using scattered translates of the Poisson kernel ⋮ Nonuniform sampling and recovery of multidimensional bandlimited functions by Gaussian radial-basis functions ⋮ Interpolation in weighted spaces of entire functions in \(\mathbb C^2\) ⋮ Riesz wavelets, tiling and spectral sets in LCA groups ⋮ Multiple lattice tiles and Riesz bases of exponentials ⋮ Exponential bases on two dimensional trapezoids

Cites Work

• Interpolation on plane sets in \({\mathbb{C}}^ 2\)
• Necessary density conditions for sampling an interpolation of certain entire functions
• The regularity of growth of entire functions whose zeros are hyperplanes
• Five short stories about the cardinal series
• Interpolation in Spaces of Entire Functions in ℂ^N
• A Class of Nonharmonic Fourier Series
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