# Landau's necessary density conditions for LCA groups

Source: [Landau's necessary density conditions for LCA groups](<https://www.sota2.com/research/paper/68fa4ef11e209131ce95f9f0>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:55:22.465Z

Authors: K. Gr\\"ochenig, G. Kutyniok, K. Seip

Published: 2008-03-25T11:11:19.000Z

## Abstract

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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/0803.3529>)

[PDF](<https://arxiv.org/pdf/0803.3529.pdf>)