Landau's necessary density conditions for LCA groups

Details Landau's necessary density conditions for LCA groups Landau's necessary density conditions for LCA groups

2008-03-25

arxiv.org/abs/0803.3529v1

J. Functional Anal. 255 (2008), 1831--1850

Mathematics

Functional Analysis

Scientific paper

H. Landau's necessary density conditions for sampling and interpolation may be viewed as a general principle resting on a basic fact of Fourier analysis: The complex exponentials $e^{i kx}$ ($k$ in $\mathbb{Z}$) constitute an orthogonal basis for $L^2([-\pi,\pi])$. The present paper extends Landau's conditions to the setting of locally compact abelian (LCA) groups, relying in an analogous way on the basics of Fourier analysis. The technicalities--in either case of an operator theoretic nature--are however quite different. We will base our proofs on the comparison principle of J. Ramanathan and T. Steger.

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