The fractional Hilbert transform, a generalization of the Hilbert transform, has been extensively studied in the literature because of its widespread application in optics, engineering, and signal processing. In the present work, we expand the fracti...
An investigation of the concept of “surveyability” as traced through the thought of Hilbert, Wittgenstein, and Turing. The communicability and reproducibility of proof, with certainty, are seen as earmarked by the “surveyability&rdq...
This paper studies the properties of the Fourier transform of the fuzzy function, and extends the classical Poisson integral formula on the half plane to the fuzzy case, obtaining the composition of the fuzzy set generated by a point in the complex f...
Frames for Hilbert spaces are interesting for mathematicians but also important for applications in, e.g., signal analysis and physics. In both mathematics and physics, it is natural to consider a full scale of spaces, and not only a single one. In t...
In this paper, we use soft linear operators to introduce the notion of discrete frames on soft Hilbert spaces, which extends the classical notion of frames on Hilbert spaces to the context of algebraic structures on soft sets. Among other results, we...
This manuscript aims to provide a new characterization of Sheffer stroke Hilbert algebras due to their ideals and proposes stabilizers. In the setup of the main results, we construct particular subsets of Sheffer stroke Hilbert algebras and we propos...
In this paper, we present several new inequalities for weaving frames in Hilbert spaces from the point of view of operator theory, which are related to a linear bounded operator induced by three Bessel sequences and a scalar in the set of real number...
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a time-independent Hilbe...
In this study, we obtain the
We show that Lie groups and their respective algebras, special functions and rigged Hilbert spaces are complementary concepts that coexist together in a common framework and that they are aspects of the same mathematical reality. Special functions se...
Quaternionic Hilbert spaces play an important role in applied physical sciences especially in quantum physics. In this paper, the operator valued frames on quaternionic Hilbert spaces are introduced and studied. In terms of a class of partial isometr...
We consider conditions on a given system F of vectors in Hilbert space H, forming a frame, which turn H into a reproducing kernel Hilbert space. It is assumed that the vectors in F are functions on some set Ω . We then identify conditions on these fu...
The Hilbert transform is a commonly used linear operator that separates the real and imaginary parts of an analytic signal and is employed in various fields, such as filter design, signal processing, and communication theory. However, it falls short...
Some general fixed points theorems in Hilbert spaces are proved which generalize the results from [1].
In this paper, we give the generalized Cauchy–Schwarz inequality and an extension of Buzano inequality on quasi-Hilbert C*-modules. Additionally, the upper bounds of the numerical radius of bounded adjointable operators on Hilbert C*-modules ar...
Throughout this article, we will demonstrate some new generalizations of dynamic Hilbert type inequalities, which are used in various problems involving symmetry. We develop a number of those symmetric inequalities to a general time scale. From these...
Metamaterials, or metasurfaces, allow the flexible and efficient manipulation of electromagnetic (EM) wave. Although the passive coding metasurfaces have achieved a great deal of functionality, they also need a complex design process. In this paper,...
Motivated by recent advancements in the quantum detection problem employing both discrete and continuous frames, this paper delves into a quantum detection problem utilizing g-frames within the context of quaternionic Hilbert spaces. We offer several...
A quantum injective frame is a frame capable of differentiating states based on their respective frame measurements, whereas the quantum-detection problem associated with frames endeavors to delineate all such frames. In the present paper, the concep...
Enhancer-promoter interactions (EPIs) play a significant role in the regulation of gene transcription. However, enhancers may not necessarily interact with the closest promoters, but with distant promoters via chromatin looping. Considering the spati...
The aim of this work is to adapt the methods of optical Hilbert diagnostics for the visualization and study of inverse diffusion H2/O2 flame. The diagnostic complex is implemented on the basis of the IAB-451 device with modified optical filtering. Vi...
This study advances the application of the generalized Halmos’ two projections theorem to idempotent operators on Hilbert
In this article, by using some algebraic inequalities, nabla Hölder inequalities, and nabla Jensen’s inequalities on timescales, we proved some new nabla Hilbert-type dynamic inequalities on timescales. These inequalities extend some known...
In this paper, we prove that every bounded linear operator on a separable Hilbert space has a non-trivial invariant subspace. This answers the well-known invariant subspace problem.
We investigate
In this article, we will prove some new diamond alpha Hilbert-type dynamic inequalities on time scales which are defined as a linear combination of the nabla and delta integrals. These inequalities extend some known dynamic inequalities on time scale...
We reformulate holographic space–time models in terms of Hilbert bundles over the space of the time-like geodesics in a Lorentzian manifold. This reformulation resolves the issue of the action of non-compact isometry groups on finite-dimensiona...
This paper explores the application of Hilbert topological spaces and linear operator algebra in the modelling and analysis of OFDM signals and wireless channels, where the channel is considered as a linear time-invariant (LTI) system. The wireless c...
We analyze smooth nonlinear mappings for Hilbert and Banach spaces that carry small balls to convex sets, provided that the radii of the balls are small enough. We focus on the study of new and mildly sufficient conditions for the nonlinear mapping o...
The Hilbert metric is a widely used tool for analysing the convergence of Markov processes and the ergodic properties of deterministic dynamical systems. A useful representation formula for the Hilbert metric was given by Liverani. The goal of the pr...
Fault diagnostics present a crucial technical issue in the areas of both the condition monitoring of machines and the monitoring of structural health. The identification of faults at an early stage in their development has an immense effect on the sa...
This paper is devoted to the uniqueness of solutions for a class of nonhomogeneous stationary partial differential equations related to Hamilton–Jacobi-type equations in infinite-dimensional Hilbert spaces. Specifically, the uniqueness of the v...
Hilbert-type integral inequalities, which feature a symmetric structure, are a significant class of inequalities with broad applications in the study of operator theory. Hilbert-type integral inequalities involving variable upper limit integral funct...
This manuscript develops the study of reverse Hilbert-type inequalities by applying reverse Hölder inequalities on
We establish a new inequality of Hilbert-type containing positive homogeneous kernel
In this paper, we obtain new inequalities for g-frames in Hilbert
The graph Hilbert transform (GHT) is a key tool in constructing analytic signals and extracting envelope and phase information in graph signal processing. However, its utility is limited by confinement to the graph Fourier domain, a fixed phase shift...
We study the Hilbert geometry induced by the Siegel disk domain, an open-bounded convex set of complex square matrices of operator norm strictly less than one. This Hilbert geometry yields a generalization of the Klein disk model of hyperbolic geomet...
The quantum evolution of wave functions controlled by the spectrum of Lévy random matrices is considered. An analytical treatment of quantum recurrences and revivals in the Hilbert space is performed in the framework of a theory of almost periodic fu...
In the present paper, we establish an equivalent form related to a Hilbert-type integral inequality with a non-homogeneous kernel and a best possible constant factor. We also consider the case of homogeneous kernel as well as certain operator express...
Making use of weight coefficients as well as real/complex analytic methods, an extension of a Hardy–Hilbert-type inequality with a best possible constant factor and multiparameters is established. Equivalent forms, reverses, operator expression with...
In our previous work, by combining the Hilbert scan with the symbol grouping method, efficient run-length-based entropy coding was developed, and high-efficiency image compression algorithms based on the entropy coding were obtained. However, the 2-D...
An introductory theory of frames on finite dimensional left quaternion Hilbert spaces is demonstrated along the lines of their complex counterpart.
The Hilbert transform is a well-known tool of time series analysis that has been widely used to investigate oscillatory signals that resemble a noisy periodic oscillation, because it allows instantaneous phase and frequency to be estimated, which in...
In this paper, we address Hardy–Hilbert-type inequality by virtue of constructing weight coefficients and introducing parameters. By using the Euler–Maclaurin summation formula, Abel’s partial summation formula, and differential mea...
In this article, we establish some new generalized inequalities of the Hilbert-type on time scales’ delta calculus, which can be considered similar to formulas for inequalities of Hilbert type. The major innovation point is to establish some dy...
As a classical method to deal with nonlinear and nonstationary signals, the Hilbert–Huang transform (HHT) is widely used in various fields. In order to overcome the drawbacks of the Hilbert–Huang transform (such as end effects and mode mixing) during...
The aim of this article was to provide improved estimates for the
In this paper, we establish a new Hardy–Hilbert-type inequality involving parameters composed of a pair of weight coefficients with their sum. Our result is a unified generalization of some Hardy–Hilbert-type inequalities presented in ear...
In dynamical systems, Hilbert spaces provide a useful framework for analyzing and solving problems because they are able to handle infinitely dimensional spaces. Many dynamical systems are described by linear operators acting on a Hilbert space. Unde...
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