On Sampling and Interpolation by Model Sets

Richard C, Schumacher C (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Journal of Fourier Analysis and Applications Springer Verlag (Germany)

Book Volume: 26

Journal Issue: 3

DOI: 10.1007/s00041-020-09742-w

Abstract

We refine a result of Matei and Meyer on stable sampling and stable interpolation for simple model sets. Our setting is model sets in locally compact abelian groups and Fourier analysis of unbounded complex Radon measures as developed by Argabright and de Lamadrid. This leads to a refined version of the underlying model set duality between sampling and interpolation. For rather general model sets, our methods also yield an elementary proof of stable sampling and stable interpolation sufficiently far away from the critical density, which is based on the Poisson Summation Formula.

Authors with CRIS profile

Christoph Richard Lehrstuhl für Mathematische Stochastik

Involved external institutions

Technische Universität Dortmund DE Germany (DE)

How to cite

APA:

Richard, C., & Schumacher, C. (2020). On Sampling and Interpolation by Model Sets. Journal of Fourier Analysis and Applications, 26(3). https://dx.doi.org/10.1007/s00041-020-09742-w

MLA:

Richard, Christoph, and Christoph Schumacher. "On Sampling and Interpolation by Model Sets." Journal of Fourier Analysis and Applications 26.3 (2020).

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