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Related papers: Weyl Quantization of Fractional Derivatives

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Based on the Riemann-Liouville derivatives with respect to functions taking values in the set of hyperbolic numbers, we consider a novel bicomplex proportional fractional $(\vartheta,\varphi)-$weighted Cauchy-Riemann operator, involving…

Complex Variables · Mathematics 2023-08-31 José Oscar González-Cervantes , Juan Adrián Ramírez-Belman , Juan Bory-Reyes

In this paper we use the orthogonal system of the Jacobi polynomials as a tool to study the Riemann-Liouville fractional integral and derivative operators on a compact of the real axis.This approach has some advantages and allows us to…

Functional Analysis · Mathematics 2020-02-06 M. V. Kukushkin

The ongoing progress in quantum technologies has fueled a sustained exploration of their potential applications across various domains. One particularly promising field is quantitative finance, where a central challenge is the pricing of…

Quantum Physics · Physics 2025-10-23 Fernando Alonso , Álvaro Leitao , Carlos Vázquez

The main goal of this paper is to construct a proportional analogues of the quaternionic fractional Fueter-type operator recently introduced in the literature. We start by establishing a quaternionic version of the well-known proportional…

Complex Variables · Mathematics 2023-11-14 José Oscar González-Cervantes , Juan Bory-Reyes

Using the concept of fractional derivatives of Riemann$-$Liouville on time scales, we first introduce right fractional Sobolev spaces and characterize them. Then, we prove the equivalence of some norms in the introduced spaces, and obtain…

Functional Analysis · Mathematics 2022-02-22 Xing Hu , Yongkun Li

In this paper, a Sturm-Liouville boundary value problem equiped with conformable fractional derivates is considered. We give some uniqueness theorems for the solutions of inverse problems according to the Weyl function, two given spectra…

Classical Analysis and ODEs · Mathematics 2022-03-23 A. Sinan Ozkan , İbrahim Adalar

Global dimensions for fusion categories defined by a pair (G,k), where G is a Lie group and k a positive integer, are expressed in terms of Lie quantum superfactorial functions. The global dimension is defined as the square sum of quantum…

Quantum Algebra · Mathematics 2014-05-22 Robert Coquereaux

We develop a quantization method, that we name decomposable Weyl quantization, which ensures that the constants of motion of a prescribed finite set of Hamiltonians are preserved by the quantization. Our method is based on a structural…

Mathematical Physics · Physics 2020-04-20 Fabian Belmonte

We investigate quasi-hermitian quantum mechanics in phase space using standard deformation quantization methods: Groenewold star products and Wigner transforms. We focus on imaginary Liouville theory as a representative example where exact…

Quantum Physics · Physics 2008-11-26 Thomas Curtright , Andrzej Veitia

Approximation theory is a substantial field of mathematical analysis that emerged in the 19th century and has been developed by mathematicians across the globe ever since. Its importance has increased over time, as it provides solutions to…

General Mathematics · Mathematics 2025-01-22 Reşat Aslan

This article develops a variational formulation of relativistic nature applicable to the quantum mechanics context. The main results are obtained through basic concepts on Riemannian geometry. Standards definitions such as vector fields and…

Analysis of PDEs · Mathematics 2019-06-13 Fabio Botelho

Compared to the the classical first-order Gr\"unwald-Letnikov formula at time $t_{k+1} (\textmd{or}\, t_{k})$, we firstly propose a second-order numerical approximate scheme for discretizing the Riemann-Liouvile derivative at time…

Numerical Analysis · Mathematics 2017-11-21 Hengfei Ding , Changpin Li

In classical complex analysis analyticity of a complex function $f$ is equivalent to differentiability of its real and imaginary parts $u$ and $v$, respectively, together with the Cauchy-Riemann equations for the partial derivatives of $u$…

Functional Analysis · Mathematics 2019-06-24 S ter Horst , E. M. Klem

This work develops a magnetic pseudodifferential calculus for super operators OpA(F); these map operators onto operators (as opposed to Lp functions onto Lq functions). Here, F could be a tempered distribution or a H\"ormander symbol. An…

Mathematical Physics · Physics 2022-11-09 Gihyun Lee , Max Lein

Integral transforms arising from the separable solutions to the Helmholtz differential equation are presented. Pairs of these integral transforms are related via Plancherel theorem and, ultimately, any of these integral transforms may be…

Analysis of PDEs · Mathematics 2016-08-14 B. M. Rodríguez-Lara

Quantum channels, a subset of quantum maps, describe the unitary and non-unitary evolution of quantum systems. We study a generalization of the concept of Pauli maps to the case of multipartite high dimensional quantum systems through the…

Quantum Physics · Physics 2024-04-25 Tomas Basile , Jose Alfredo de Leon , Alejandro Fonseca , Francois Leyvraz , Carlos Pineda

Weyl quantization and related semiclassical techniques can be used to study conduction properties of crystalline solids subjected to slowly-varying, external electromagnetic fields. The case where the external magnetic field is constant, is…

Mathematical Physics · Physics 2015-08-18 Max Lein

We first prove the equivalence of two definitions of Riemann-Liouville fractional integral on time scales, then by the concept of fractional derivative of Riemann-Liouville on time scales, we introduce fractional Sobolev spaces,…

Classical Analysis and ODEs · Mathematics 2022-05-27 Xing Hu , Yongkun Li

For quantum systems with two dimensional configuration space we construct a physical radial momentum observable. Rescaling the radius we find the dilatonic degrees of freedom form a Weyl algebra. With this we construct the radial Wigner…

Quantum Physics · Physics 2008-11-26 J. Twamley

Quantum Euclidean spaces, as Moyal deformations of Euclidean spaces, are the model examples of noncompact noncommutative manifold. In this paper, we study the quantum Euclidean space equipped with partial derivatives satisfying canonical…

Operator Algebras · Mathematics 2019-08-22 Li Gao , Marius Junge , Edward McDonald