Related papers: Continuous Frames, Function Spaces, and the Discre…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
A problem of Banach asks whether every infinite-dimensional Banach space which is isomorphic to all its infinite-dimensional subspaces must be isomorphic to a separable Hilbert space. In this paper we prove a result of a Ramsey-theoretic…
A discrete frame for $L^2({\mathbb R}^d)$ is a countable sequence $\{e_j\}_{j\in J}$ in $L^2({\mathbb R}^d)$ together with real constants $0<A\leq B< \infty$ such that $$ A\|f\|_2^2 \leq \sum_{j\in J}|\langle f,e_j \rangle |^2 \leq…
The concept of frames, initially introduced by Duffin and Schaeffer, gained substantial recognition decades later when Daubechies, Grossman, and Meyer highlighted its significance. Since then, frame theory has become a fundamental and…
In this paper we introduced the concept of continuous relay fusion frames in Hilbert spaces. And we define the dual frames for continuous relay fusion frames. Finally we study the perturbation probleme of continuous relay fusion frames.
This paper is concerned with the implications of sufficient conditions ensuring that a perturbation of a frame is again a frame. We emphasize how stability of frames is fundamental for numerical applications and we discuss in particular the…
We develop a systematic algorithmic framework that unites global and local classification problems using index sets. We prove that the classification problem for continuous (binary) regular functions among almost everywhere linear,…
We develop the theory of frames and Parseval frames for finite-dimensional vector spaces over the binary numbers. This includes characterizations which are similar to frames and Parseval frames for real or complex Hilbert spaces, and the…
In solving scientific, engineering or pure mathematical problems one is often faced with a need to approximate the function of a given class by the linear combination of a preferably small number of functions that are localised one way or…
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.…
In this paper, we will introduce the concept of a continuous K-biframe for Hilbert spaces and we present various examples of continuous K-biframes. Furthermore, we investigate their characteristics from the perspective of operator theory by…
Given a frame in a finite dimensional Hilbert space we construct additive perturbations which decrease the condition number of the frame. By iterating this perturbation, we introduce an algorithm that produces a tight frame in a finite…
This chapter offers a detailed survey on intrinsically localized frames and the corresponding matrix representation of operators. We re-investigate the properties of localized frames and the associated Banach spaces in full detail. We…
Fusion frames are a very active area of research today because of their myriad of applications in pure mathematics, applied mathematics, engineering, medicine, signal and image processing and much more. They provide a great flexibility for…
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
Concentration compactness method is a powerful techniques for establishing existence of minimizers for inequalities and of critical points of functionals in general. The paper gives a functional-analytic formulation for the method in Banach…
Random sets are used to get a continuous partition of the cardinality of the union of many overlapping sets. The formalism uses M\"obius transforms and adapts Shapley's methodology in cooperative game theory, into the context of set theory.…
This paper is a contribution to the theory of dynamical sampling. Our purpose is twofold. We first consider representations of sequences in a Hilbert space in terms of iterated actions of a bounded linear operator. This generalizes recent…
We consider Banach spaces equipped with a set of strongly continuous bounded semigroups satisfying certain conditions. Using these semigroups we introduce an analog of a modulus of continuity and define analogs of Besov norms. A…
Coorbit space theory is an abstract approach to function spaces and their atomic decompositions. The original theory developed by Feichtinger and Gr{\"o}chenig in the late 1980ies heavily uses integrable representations of locally compact…