Frames on Hilbert C*-modules have been defined for unital C*algebras by Frank and Larson [5] and operator-valued frames on a Hilbert space have been studied in [8]. The goal of this paper is to introduce operatorvalued frames on a Hilbert C*-module for a σ-unital C*-algebra. Theorem 1.4 reformulates the definition given in [5] in terms of a series of rank-one operators converging in the strict ...

Theory of fractional calculus with singular and non-singular kernels is pioneering has garnered significant interest recently. Fair amount literature on the qualitative properties differential integral equations involving different types operators available. This manuscript aims to analyze stability a class nonlinear equation in terms Atangana-Baleanu-Caputo operator. Sufficient conditions for ...

We study Weyl-Heisenberg (=Gabor) expansions for either L2(IR ) or a subspace of it. These are expansions in terms of the spanning set X = (EM φ : k ∈ K, l ∈ L,φ ∈ Φ), where K and L are some discrete lattices in IR, Φ ⊂ L2(IR ) is finite, E is the translation operator, and M is the modulation operator. Such sets X are known as WH systems. The analysis of the “basis” properties of WH systems (e....

We study Weyl-Heisenberg (=Gabor) expansions for either L 2 (IR d) or a subspace of it. These are expansions in terms of the spanning set where K and L are some discrete lattices in IR d , L 2 (IR d) is nite, E is the translation operator, and M is the modulation operator. Such sets X are known as WH systems. The analysis of the \basis" properties of WH systems (e.g. being a frame or a Riesz ba...

Abstract As generalizations of g-frames and controlled frames, the theory has been deeply studied. This paper addresses dual in Hilbert spaces. We first present some equivalent characterizations g-frames. Then, we introduce concepts operator, get properties them. Finally, obtain for a given g-frame by method operator theory.