  In this paper, we give a multiplication operator representation of bounded
self-adjoint operators T on a Hilbert space H such that -- is a frame for H,
for some -- . We state a necessary condition in order for a frame -- to have a
representation of the form -- . Frame sequence -- with the synthesis operator
U, have also been characterized in terms of the behavior spectrum of -- . Next,
using the operator response of an element with respect to a unit vector in H,
frames -- of the form -- are characterized. We also consider stability frames
as -- . Finally, we conclude this note by raising a conjecture connecting frame
theory and operator theory
