Sampling in unitary invariant subspaces associated to LCA groups Articles uri icon

publication date

  • December 2017

start page

  • 1725

end page

  • 1745

issue

  • 4

volume

  • 72

International Standard Serial Number (ISSN)

  • 1422-6383

Electronic International Standard Serial Number (EISSN)

  • 1420-9012

abstract

  • In this paper a sampling theory for unitary invariant subspaces associated to locally compact abelian (LCA) groups is deduced. Working in the LCA group context allows to obtain, in a unified way, sampling results valid for a wide range of problems which are interesting in practice, avoiding also cumbersome notation. Along with LCA groups theory, the involved mathematical technique is that of frame theory which meets matrix analysis when appropriate dual frames are computed.

keywords

  • LCA groups
    unitary representation of a LCA group
    unitary-invariant subspaces
    frames
    dual frames
    sampling expansions