Related papers: Group-Frames for Banach Spaces

Let $K$ be a compact group, and let $\rho$ be a representation of $K$ on a Hilbert space $\mathcal{H}_\rho$. We classify invariant subspaces of $\mathcal{H}_\rho$ in terms of range functions, and investigate frames of the form $\{\rho(\xi)…

Notion of frames and Bessel sequences for metric spaces have been introduced. This notion is related with the notion of Lipschitz free Banach spaces. \ It is proved that every separable metric space admits a metric $\mathcal{M}_d$-frame.…

Motivated by a general dilation theory for operator-valued measures, framings and bounded linear maps on operator algebras, we consider the dilation theory of the above objects with special structures. We show that every operator-valued…

This paper generalizes results for alternate dual frames in Hilbert spaces on the situation of a Banach space. Additionally some properties of synthesys operator associated with alternate dual frame are investigated. The main result is that…

This paper studies Schauder frames in Banach spaces, a concept which is a natural generalization of frames in Hilbert spaces and Schauder bases in Banach spaces. The associated minimal and maximal spaces are introduced, as are shrinking and…

We consider dual frames generated by actions of countable discrete groups on a Hilbert space. Module frames in a class of modules over a group algebra are shown to coincide with a class of ordinary frames in a representation of the group.…

We define the frame potential for a Schauder frame on a finite dimensional Banach space as the square of the $2$-summing norm of the frame operator. As is the case for frames for Hilbert spaces, we prove that the frame potential can be used…

We introduce a new concept of frame operators for Banach spaces we call a Hilbert-Schauder frame operator. This is a hybird between standard frame theory for Hilbert spaces and Schauder frame theory for Banach spaces. Most of our results…

We extend the theory of operator-valued frames (resp. bases), hence the theory of frames (resp. bases), for Hilbert spaces and Hilbert C*-modules, in two folds. This extension leads us to develop the theory of operator-valued frames (resp.…

This paper is concerned with the characterization of $\alpha$-modulation spaces by Banach frames, i.e., stable and redundant non-orthogonal expansions, constituted of functions obtained by a suitable combination of translation, modulation…

The duality principle for group representations developed in \cite{DHL-JFA, HL_BLM} exhibits a fact that the well-known duality principle in Gabor analysis is not an isolated incident but a more general phenomenon residing in the context of…

A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous superpositions. Associated to a given continuous frame we construct certain Banach spaces. Many classical function…

This paper provides a self-contained exposition of coorbit spaces associated to integrable group representations and quasi-Banach function spaces, and at the same time extends and simplifies previous work. The main results provide an…

Difficulty in the construction of dual frames for a given Hilbert space led to the introduction of approximately dual frames in Hilbert spaces by Christensen and Laugesen. It becomes even more difficult in Banach spaces to construct duals.…

For the solution of operator equations, Stevenson introduced a definition of frames, where a Hilbert space and its dual are {\em not} identified. This means that the Riesz isomorphism is not used as an identification, which, for example,…

We give an operator-algebraic treatment of theory of p-approximate Schuader frames which includes the theory of operator-valued frames by Kaftal, Larson, and Zhang [\textit{Trans. AMS., 2009}], G-frames by Sun [JMAA, 2006], factorable weak…

Gabor frames with Hermite functions are equivalent to sampling sequences in true Fock spaces of polyanalytic functions. In the L^2-case, such an equivalence follows from the unitarity of the polyanalytic Bargmann transform. We will…

In this paper, we introduce, for a separable Banach spacea new notion of besselian paires and of besselian Schauder frames for which we prove for some fundamental results.

The duality principle for Gabor frames states that a Gabor sequence obtained by a time-frequency lattice is a frame for $L^{2}(\R^{d})$ if and only if the associated adjoint Gabor sequence is a Riesz sequence. We prove that this duality…

The goal of this paper is to study band-dominated operators on Banach spaces with Schauder basis with respect to uniformly locally finite metric spaces as well as the Banach algebras generated by them: the so called uniform Roe algebras. We…