Linear combinations of frame generators in systems of translates.

CARLOS CABRELLI, CAROLINA MOSQUERA, VICTORIA PATERNOSTRO

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2014 vol. 413 p. 776 - 788

0022-247X

A finitely generated shift invariant space $V$ is a closed subspace of  $L^2(R^d)$ that can be generated by the integer translates of a finite number of functions. A set of frame generators for $V$ is a set of functions whose  integer translates form a frame for $V$.In this note we give necessary and sufficient conditions in order that a minimal set of frame generators can be obtained by taking linear combinations of the given frame generators.Surprisingly the results are very different to the recently studied case when the property to be a frame is not required.