Results 41 to 50 of about 3,271,458 (133)
Spectral Analysis of the Dunkl–Bessel Laplacian and Its Applications
Journal of Function Spaces, Volume 2026, Issue 1, 2026.In this paper, we develop a concrete von Neumann spectral analysis of the Dunkl–Bessel Laplacian −Δκ,αW, considered through its maximal even distributional realization on Lκ,α2,ℝ+d+1. We first prove that this realization is nonnegative and self‐adjoint and that its spectrum coincides with its continuous spectrum and is equal to [0, +∞), whereas its ...
Abdelilah El Mourni +3 more
wiley +1 more source
On the t-Transformation of Free Convolution
MathematicsThe study of the stability of measure families under measure transformations, as well as the accompanying limit theorems, is motivated by both fundamental and applied probability theory and dynamical systems. Stability analysis tries to uncover invariant
Shokrya S. Alshqaq +2 more
doaj +1 more source
Journal of Function Spaces, Volume 2026, Issue 1, 2026.In this paper, we develop a comprehensive analytical framework for generalized nonlinear, nonhomogeneous Volterra integral equations and fractional differential equations in b‐metric spaces equipped with amorphous binary relations. By introducing an enriched (f, ϕ, ψ, s)‐functional contraction, we extend classical contractive conditions to accommodate ...
D. Srinivasan +2 more
wiley +1 more source
Notes on the Free Additive Convolution
AxiomsThe investigation of free additive convolution is a key concept in free probability theory, offering a framework for studying the sum of freely independent random variables.
Shokrya S. Alshqaq +2 more
doaj +1 more source
A Two-Parameter Extension of the Va Deformation of Probability Measures
SymmetryThis article proposes a single-deformation scheme for probability measures that simultaneously encompasses two classical deformations from free probability: the Va deformation (a∈R) and the Tc deformation (c∈R). The associated operator, written as W(a,c),
F. Alsharari, R. Fakhfakh, G. Alomani
semanticscholar +1 more source
Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract The representation of an analytic function as a series involving q$q$‐polynomials is a fundamental problem in classical analysis and approximation theory [Ramanujan J. 19 (2009), no. 3, 281–303]. In this paper, our investigation is focusing on q$q$‐analog complex Hermite polynomials, which were motivated by Ismail and Zhang [Adv. Appl.
Jian Cao
wiley +1 more source
Approximating the Stieltjes Integral of Bounded Functions and Applications for Three Point Quadrature Rules [PDF]
, 2007 Sharp error estimates in approximating the Stieltjes integral with bounded integrands and bounded integrators respectively, are given.
Dragomir, Sever S
core +1 more source
Studies on Cauchy–Stieltjes Kernel Families
MathematicsIn the setting of Cauchy–Stieltjes kernel (CSK) families, this study provides some features of free Poisson, free Gamma, and free Binomial laws, as well as some innovative limit theorems linked to Fermi convolution.
Abdulmajeed Albarrak +2 more
doaj +1 more source
Extended (s, t)-Transformation of Probability Measures
SymmetryIn this paper, we introduce two analytic deformations of probability measures that unify and extend two classical deformations from free probability theory, namely the T=(s,t)-deformation UT and the Ta-deformation, where a,t∈R and s>0.
R. Fakhfakh +2 more
semanticscholar +1 more source
Nonlinear shrinkage test on a large‐dimensional covariance matrix
Statistica Neerlandica, Volume 79, Issue 1, February 2025.This paper is concerned with deriving a new test on a covariance matrix which is based on its nonlinear shrinkage estimator. The distribution of the test statistic is deduced under the null hypothesis in the large‐dimensional setting, that is, when p/n→c∈(0,+∞) with p variables and n samples both tending to infinity.
Taras Bodnar +2 more
wiley +1 more source