Continuous and discrete dynamical sampling'

DIAZ MARTIN, ROCIO; MEDRI, IVAN; MOLTER, URSULA

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2021 vol. 499

0022-247X

In this paper we study the continuous dynamical sampling problem at infinite time in a complex Hilbert space H. We find necessary and sufficient conditions on a bounded linear operator A, and a set of vectors G, in order to obtain that {e^{tA}} is a semi-continuous frame for H. We study if it is possible to discretize the time variable t and still have a frame for H. We also relate the continuous iteration e^{tA} on a set G, to the discrete iteration (A´)^n on G´, for an adequate operator A´ and set G´.