Related papers: Dual Fusion Frames
Novel analysis of finite dimensional Hilbert space is outlined. The approach bypasses general, inherent, difficulties present in handling angular variables in finite dimensional problems: The finite dimensional, d, Hilbert space operators…
Existing video stabilization methods often generate visible distortion or require aggressive cropping of frame boundaries, resulting in smaller field of views. In this work, we present a frame synthesis algorithm to achieve full-frame video…
Spectral tetris is a fexible and elementary method to construct unit norm frames with a given frame operator, having all of its eigenvalues greater than or equal to two. One important application of spectral tetris is the construction of…
This paper presents an overview of close parallels that exist between the theory of positive operator-valued measures (POVMs) associated with a separable Hilbert space and the theory of frames on that space, including its most important…
This paper presents a bicomplex version of the Spectral Decomposition Theorem on infinite dimensional bicomplex Hilbert spaces. In the process, the ideas of bounded linear operators, orthogonal complements and compact operators on bicomplex…
Certain results about frames are extended for the new frames in Hilbert C*-modules. In this paper, we introduce the notion of A-2-frames in A-2-inner product spaces and give some characterizations for these frames. Then we define the tensor…
We introduce the notion of continuous frame in n-Hilbert space which is a generalization of discrete frame in n-Hilbert space. The tensor product of Hilbert spaces is a very important topic in mathematics. Here we also introduce the concept…
The possibility of defining sesquilinear forms starting from one or two sequences of elements of a Hilbert space is investigated. One can associate operators to these forms and in particular look for conditions to apply representation…
The physics of a photonic structure is commonly described in terms of its apparent geometric dimensionality. On the other hand, with the concept of synthetic dimension, it is in fact possible to explore physics in a space with a…
The growing reliance on digital twins across various industries and domains brings with it semantic interoperability challenges. Ontologies are a well-known strategy for addressing such challenges, though given the complexity of the…
Dynamical supersymmetry breaking is considered in models which admit descriptions in terms of electric, confined, or magnetic degrees of freedom in various limits. In this way, a variety of seemingly different theories which break…
Controlled frames have been the subject of interest because of its ability to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper, we introduce the concepts of controlled g-fusion frame…
We study 3d theories determined by three-manifolds. Previously, we found that some basic 3d dualities relate to the surgeries of three-manifolds and defined gauge circles and matter circles. In this note, we discuss some operations…
The aim of this work is to study frame theory in quaternionic Hilbert spaces. We provide a characterization of frames in these spaces through the associated operators. Additionally, we examine frames of the form $\{Lu_i\}_{i \in I}$, where…
Let $A$ be an operator on {a separable } Hilbert space $\cH$, and let $G \subset \cH$. It is known that - under appropriate conditions on $A$ and $G$ - the set of iterations $F_G(A)= \{A^j \gbf \; | \; \gbf \in G, \; 0 \leq j \leq L(\gbf)…
We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building…
Frame theory is an exciting, dynamic and fast paced subject with applications in numerous fields of mathematics and engineering. In this paper we study Continuous Frame and introduce Continuous Frame with $C^{\ast}$-valued bounds. Also, we…
In this article we find a necessary and sufficient condition under which a given collection of subspace is a $J$-fusion frame for a Krein space $\mathbb{K}$. We also approximate $J$-fusion frame bounds of a $J$-fusion frame by the upper and…
The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing…
A DFT algebroid is a special case of the metric (or Vaisman) algebroid, shown to be relevant in understanding the symmetries of double field theory. In particular, a DFT algebroid is a structure defined on a vector bundle over doubled…