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Lattice Tiling and the Weyl-Heisenberg Frames
| Content Provider | Semantic Scholar |
|---|---|
| Author | Han, Deguang |
| Copyright Year | 2000 |
| Abstract | Let L and K be two full rank lattices in R. We prove that if v(L) = v(K), i.e. they have the same volume, then there exists a measurable set Ω such that it tiles R 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) ≤ v(K) then there exists a measurable set Ω 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. 1991 Mathematics Subject Classification. Primary 52C22, 52C17, 42B99, 42C30. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.math.gatech.edu/~wang/Preprints/wh.ps.Z |
| Alternate Webpage(s) | http://www.math.ust.hk/~yangwang/Reprints/wh.pdf |
| Alternate Webpage(s) | http://www.math.gatech.edu/~wang/Reprints/wh.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Frame (physical object) Mathematics Subject Classification Pack unit Tiling window manager Wigner–Weyl transform |
| Content Type | Text |
| Resource Type | Article |
