Density of certain families of functions in L 2 (mu).

JUAN MIGUEL MEDINA; BRUNO CERNUSCHI FRÍAS

Bahía Blanca

Congreso; LXV Reunión de Comunicaciones Científicas de la Unión Matemática Argentina; 2016

Unión Matemática Argentina, UNS

Let µ be a regular finite non-negative Borel measure on [−π, π] or R. For appropriate f1, . . . , fm ∈ L2(µ) we give necessary and sufficient conditions for the set of funtions S ={fr e^imn . }_r=1m...,m,n∈Zto be complete in the space L2(µ). Conditions are also given on S to constitutea frame sequence or an unconditional basis. These results are closely related to the problem of finding conditions for a multi-channel sampling scheme for wide sense stationary random processes.