Lattice tiling and the Weyl-Heisenberg frames

    Authors

    D. G. Han;Y. Wang

    Comments

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    Abbreviated Journal Title

    Geom. Funct. Anal.

    Keywords

    SETS; Mathematics

    Abstract

    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.

    Journal Title

    Geometric and Functional Analysis

    Volume

    11

    Issue/Number

    4

    Publication Date

    1-1-2001

    Document Type

    Article

    Language

    English

    First Page

    742

    Last Page

    758

    WOS Identifier

    WOS:000172535800004

    ISSN

    1016-443X

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