Lattice tiling and the Weyl-Heisenberg frames
Abbreviated Journal Title
Geom. Funct. Anal.
Let L and K be two full rank lattices in R-d. We prove that if v(L) = v(K), i.e. they have the same volume, then there exists a measurable set Omega such that it tiles R-d by both L and K. A counterexample shows that the above tiling result is false for three or more lattices. Furthermore, we prove that if v(L) less than or equal to v(K) then there exists a measurable set Omega such that it tiles by L and packs by K. Using these tiling results we answer a well-known question on the density property of Weyl-Heisenberg frames.
Geometric and Functional Analysis
"Lattice tiling and the Weyl-Heisenberg frames" (2001). Faculty Bibliography 2000s. 8020.