Related papers: Frames for model spaces

Finite frames can be viewed as mass points distributed in $N$-dimensional Euclidean space. As such they form a subclass of a larger and rich class of probability measures that we call probabilistic frames. We derive the basic properties of…

Inspired by the work of Bemrose et al. \cite{Be16}, we delve into the study of weaving frames in Krein spaces. This paper presents a comprehensive exploration of various properties and characterizations of Krein space weaving frames. In…

While the last five years have seen considerable progress in understanding the internal representations of deep learning models, many questions remain. This is especially true when trying to understand the impact of model design choices,…

The notion of g-frames for Hilbert spaces was introduced and studied by Wenchang Sun [16] as a generalization of the notion of frames. In this paper, we define computable g-frames in computable Hilbert spaces and obtain computable versions…

Frames and Bessel sequences in Fr\'echet spaces and their duals are defined and studied. Their relation with Schauder frames and representing systems is analyzed. The abstract results presented here, when applied to concrete spaces of…

An introductory theory of frames on finite dimensional quaternion Hilbert spaces is demonstrated along the lines of their complex counterpart.

In this paper we discuss some topics related to the general theory of frames. In particular we focus our attention to the existence of different 'reconstruction formulas' for a given vector of a certain Hilbert space and to some refinement…

In this chapter we survey two topics that have recently been investigated in frame theory. First, we give an overview of the class of scalable frames. These are (finite) frames with the property that each frame vector can be rescaled in…

Vector-valued discrete Fourier transforms (DFTs) and ambiguity functions are defined. The motivation for the definitions is to provide realistic modeling of multi-sensor environments in which a useful time-frequency analysis is essential.…

A new notion of dual fusion frame has been recently introduced by the authors. In this article that notion is further motivated and it is shown that it is suitable to deal with questions posed in a finite-dimensional real or complex Hilbert…

In this paper, we introduce and study the frames in separable quaternionic Hilbert spaces. Results on the existence of frames in quaternionic Hilbert spaces have been given. Also, a characterization of frame in quaternionic Hilbert spaces…

Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…

The ability to construct, use, and revise models is a crucial experimental physics skill. Many existing frameworks describe modeling in science education at introductory levels. However, most have limited applicability to the context of…

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)…

G-frames are generalized frames which include ordinary frames, bounded invertible linear operators, as well as many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. G-frames are natural…

Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…

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,…

Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…

Machine Learning algorithms have had a profound impact on the field of computer science over the past few decades. These algorithms performance is greatly influenced by the representations that are derived from the data in the learning…

This article suggests that thinking about the role of reference frames can provide new insight into Extended Wigner's Friend scenarios. This involves appealing to symmetries to make a principled distinction between properties of a system…