The graph Fourier transform (GFT) is in general dense and requires O(n) time to compute and O(n) memory space to store. In this paper, we pursue our previous work on the approximate fast graph Fourier transform (FGFT). The FGFT is computed via a truncated Jacobi algorithm, and is defined as the product of J Givens rotations (very sparse orthogonal matrices). The truncation parameter, J , repres...

This paper presents a study of the morphological slope transform in the complete lattice framework. It discusses in detail the interrelationships between the slope transform at one hand and the (Young-Fenchel) conjugate and Legendre transform, two well-known concepts from convex analysis, at the other. The operators and transforms of importance here (hull operations, slope transform, support fu...

In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...

Embedding results of Sobolev type are proved for the Dunkl harmonic oscillator on the line.

The aim of this paper is to establish a few qualitative uncertainty principles for the windowed Opdam–Cherednik transform on weighted modulation spaces associated with transform. In particular, we obtain Cowling–Price's, Hardy's and Morgan's spaces. proofs results are based versions Phragmén–Lindlöf type result several complex variables properties Gaussian kernel Jacobi–Cherednik operator.

This note encloses relatively short proofs of the following known results: the radial Dunkl process associated with a reduced system and a strictly positive multiplicity function is the unique strong solution for all time t of a stochastic differential equation of a singular drift (see [12] for the original proof and [4] for a proof under additional restrictions), the first hitting time of the ...

We introduce the Dunkl--Klein--Gordon (DKG) equation in 2D by changing standard partial derivatives Dunkl Klein--Gordon (KG) equation. show that generalization with derivative of $z$-component angular momentum is what allows separation variables DKG Then, we compute energy spectrum and eigenfunctions equations for Coulomb potential oscillator analytically from an ${\rm su}(1,1)$ algebraic point...

Abstract The main aim of this article is to study a new generalizations the Gauss hypergeometric matrix and confluent functions by using two-parameter Mittag–Leffler function. In particular, we investigate certain important properties these extended such as integral representations, differentiation formulas, beta transform, Laplace transform. Furthermore, introduce an extension Jacobi orthogona...

In this paper, we study some important basic properties of Dunkl-bounded variation functions. particular, derive a way approximating functions by smooth and establish version the Gauss–Green Theorem. We also Dunkl BV capacity investigate measure theoretic properties, moreover, show that Hausdorff codimension one have same null sets. Finally, develop characterization heat semigroup space, thereb...