### CAS Seminar

# Alexandros Gelastopoulos

### (Jacobs University)

## "Sampling in shift invariant spaces"

** Date: ** |
Wed, April 3, 2013 |

** Time: ** |
14:15 |

** Place: ** |
Research I Seminar Room |

**Abstract:** The classical Shannon sampling theorem states that bandlimited functions can be reconstructed from their values on regularly spaced points. This result has been extended from spaces of bandlimited functions to shift invariant subspaces (SIS) of L^{2}(R), that is spaces spanned by the integer shifts of a set of generators. Work by Sun and Zhou treats the case of a single generator whose integer shifts form a frame for the SIS, as well as the case of a finite number of generators with the restriction that their integer shifts form a Riesz basis for the SIS. We study a common generalization of these two cases, namely sampling in SIS generated by a finite number of L^{2} functions, whose integer shifts form merely a frame for the SIS.