Related papers: Cyclic frames in finite-dimensional Hilbert spaces
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…
Frames in separable Hilbert spaces gives stable analysis and reconstruction of each vector in the underlying space. In this paper, we study frame conditions for a collection of matrix-valued functions obtained by non-uniform shifts. We give…
This paper is a significant part of a general project aimed to classify all irreducible representations of finite quasi-simple groups over an algebraically closed field, in which the image of at least one element is represented by an almost…
In this paper the notion of the rigid frame of reference within special relativity is analysed. Three definitions of rigidity are formulated. By using several examples of non-inertial frames, it is shown that these definitions are not…
A complete classification and character formulas for finite-dimensional irreducible representations of the rational Cherednik algebra of type A is given. Less complete results for other types are obtained. Links to the geometry of affine…
In this paper it is shown that the space of tight geodesic segments connecting any two vertices in a complex of cycles has finite, uniformly bounded dimension. The dimension is defined in terms of a discrete analogue of Jacobi fields, which…
Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…
This paper aims to explore the concept of continuous \( K \)-frames in quaternionic Hilbert spaces. First, we investigate \( K \)-frames in a single quaternionic Hilbert space \( \mathcal{H} \), where \( K \) is a right $\mathbb{H}$-linear…
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 consider "cubes" in products of finite cyclic groups and we study their tiling and spectral properties. (A set in a finite group is called a tile if some of its translates form a partition of the group and is called spectral if it admits…
We show that the cyclic and epicyclic categories which play a key role in the encoding of cyclic homology and the lambda operations, are obtained from projective geometry in characteristic one over the infinite semifield F of "max-plus…
Despite decades of work, gaining a first-principle understanding of amorphous materials remains an extremely challenging problem. However, recent theoretical breakthroughs have led to the formulation of an exact solution in the mean-field…
We discuss and prove a number of results for calculating characteristic cycles, or graded, enriched characteristic cycles. We concentrate particularly on results related to hypersurfaces.
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and quantum circuits are naturally interpretable in such structures. We…
High-Dimensional Dynamic Factor Models are presented in detail: The main assumptions and their motivation, main results, illustrations by means of elementary examples. In particular, the role of singular ARMA models in the theory and…
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and circuits are naturally interpretable in such structures. We consider…
With the help of hypergeometric functions over finite fields, we study some arithmetic properties of cyclotomic matrices involving characters and binary quadratic forms over finite fields. Also, we confirm some related conjectures posed by…
This paper is a significant contribution to a general programme aimed to classify all projective irreducible representations of finite simple groups over an algebraically closed field, in which the image of at least one element is…
Using the dynamical system approach, we describe the general dynamics of cosmological scalar fields in terms of critical points and heteroclinic lines. It is found that critical points describe the initial and final states of the scalar…
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…