Related papers: Algebraic Image Processing
It is well known that the unboundedness of operators in Hilbert space entails domain troubles. It is also well known that most domain troubles can be surmounted by extending the Hilbert space to a rigged Hilbert space. In this note, we…
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…
Operator-valued frames are natural generalization of frames that have been used in quantum computing, packets encoding, etc. In this paper, we focus on developing the theory about operator-valued frames for finite Hilbert spaces. Some…
The Paradigms introduced in philosophy of science one century ago are shown to be quite more satisfactory of that introduced by Galileo. This is particularly evident in the physics based on Hilbert Spaces and related mathematical structures…
We develop a graphical notation to introduce classical Lie algebras. Although this paper deals with well-known results, our pictorial point of view is slightly different to the traditional one. Our graphical notation is fairly elementary…
In this paper, we introduce a new concept of K-biframes for Hilbert spaces. We then examine several characterizations with the assistance of a biframe operator. Moreover, we investigate their properties from the perspective of operator…
The aim of this paper is to present remarkable classes of Lie-admissible algebras containing in particular the associative algebras, the Vinberg algebras and pre-Lie algebras. We determine the associated quadratic operads and their dual…
Frames play an important role in various practical problems related to signal and image processing. In this paper, we define computable frames in computable Hilbert spaces and obtain computable versions of some of their characterizations.…
In this paper, we introduce and study frame of operators in quaternionic Hilbert spaces as a generalization of g frames which in turn generalized various notions like Pseduo frames, bounded quasi-projectors and frame of subspaces (fusion…
In this paper we introduce and study some Hilbert-type operators acting from the function spaces into the sequence spaces. We give some sufficient and necessary conditions for the boundedness and compactness of these Hilbert-type operators.…
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…
The algebra of functions on kappa-Minkowski noncommutative spacetime is studied as algebra of operators on Hilbert spaces. The representations of this algebra are constructed and classified. This new approach leads to a natural construction…
All-optical image processing offers a high-speed, energy-efficient alternative to conventional electronic systems by leveraging the wave nature of light for parallel computation. However, traditional optical processors rely on bulky…
In this master thesis, I discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science.
The aim of this paper is to provide a coherent framework for transforming boundary pairs of digital images from one resolution to another without knowledge of the full images. It is intended to facilitate the simultaneous usage of…
This note recapitulates and expands the contents of a tutorial on the mathematical theory of algebraic effects and handlers which I gave at the Dagstuhl seminar 18172 "Algebraic effect handlers go mainstream". It is targeted roughly at the…
Convergence of operators acting on a given Hilbert space is an old and well studied topic in operator theory. The idea of introducing a related notion for operators acting on arying spaces is natural. However, it seems that the first…
This paper concerns dual frames multipliers, i.e. operators in Hilbert spaces consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames, respectively. The goal of the…
The object recognition is a complex problem in the image processing. Mathematical morphology is Shape oriented operations, that simplify image data, preserving their essential shape characteristics and eliminating irrelevancies. This paper…
The study of operator algebras on Hilbert spaces, and C*-algebras in particular, is one of the most active areas within Functional Analysis. A natural generalization of these is to replace Hilbert spaces (which are $L^2$-spaces) with…