Finite Sampling in Multiple Generated U-Invariant Subspaces Articles uri icon

publication date

  • April 2016

start page

  • 2203

end page

  • 2212

issue

  • 4

volume

  • 62

International Standard Serial Number (ISSN)

  • 0018-9448

Electronic International Standard Serial Number (EISSN)

  • 1557-9654

abstract

  • The relevance in a sampling theory of U-invariant subspaces of a Hilbert space H, where U denotes a unitary operator on H, is nowadays a recognized fact. Indeed, shift-invariant subspaces of L-2(R) become a particular example; periodic extensions of finite signals also provide a remarkable example. As a consequence, the availability of an abstract U-sampling theory becomes a useful tool to handle these problems. In this paper, we derive a sampling theory for finite dimensional multiple generated U-invariant subspaces of a Hilbert space H. As the involved samples are identified as frame coefficients in a suitable euclidean space, the relevant mathematical technique is that of the finite frame theory. Since finite frames are nothing but spanning sets of vectors, the used technique naturally meets matrix analysis.

keywords

  • finite u-invariant subspaces; finite frames; dual frames; moore-penrose pseudo-inverse; left-inverses; shift-invariant; spaces; reconstruction