FRAMES FOR HILBERT SPACES WITH RESPECT TO 1-SUM OF FINITE-DIMENSIONAL SPACES
PAVEL A. TEREKHIN · Poincare Journal of Analysis and Applications · 2024
The classic definition of a frame by Duffin and Schaeffer is well known and very useful in analysis and its applications.There are many examples of constructing frames based on classical systems of functions.However, among some function systems, for example, for sequences of discretized values of the reproducing kernel of a Hilbert space, Duffin and Schaeffer frames do not exist.Therefore, from the point of view of the construction of series expansions of type h = ∞ n=1 cnfn, it turned out to be productive to use the more general concept of a frame in the situation of a Hilbert space and, especially, a Banach space.In this regard, we mention Aldroubi concept of the p-frame and its subsequent generalizations.In this paper we consider frames with respect to the ℓ 1 -sum of finite-dimensional spaces, give some examples and study some properties of such frames.