Title

Lattice Tiling And The Weyl-Heisenberg Frames

Abstract

Let ℒ and script K be two full rank lattices in ℝd. We prove that if v(ℒ) = v(script K), i.e. they have the same volume, then there exists a measurable set Ω such that it tiles ℝd by both ℒ and script K. A counter-example shows that the above tiling result is false for three or more lattices. Furthermore, we prove that if v(ℒ) ≤ v(script K) then there exists a measurable set Ω such that it tiles by ℒ and packs by script K. Using these tiling results we answer a well-known question on the density property of Weyl-Heisenberg frames.

Publication Date

1-1-2001

Publication Title

Geometric and Functional Analysis

Volume

11

Issue

4

Number of Pages

742-758

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/PL00001683

Socpus ID

0035541302 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0035541302

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