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We use the stabilization functors to study the combinatorial aspects of the $F$-polynomial of a representation of any finite-dimensional basic algebra. We characterize the vertices of their Newton polytopes. We give an explicit formula for…

Representation Theory · Mathematics 2021-08-04 Jiarui Fei

Given a real closed polytope $P$, we first describe the Fourier transform of its indicator function by using iterations of Stokes' theorem. We then use the ensuing Fourier transform formulations, together with the Poisson summation formula,…

Combinatorics · Mathematics 2018-08-02 Ricardo Diaz , Quang-Nhat Le , Sinai Robins

Several versions of the Fourier transform have been formulated in the framework of Clifford algebra. We present a (Clifford-Fourier) transform, constructed using the geometric properties of Clifford algebra. We show the corresponding…

Functional Analysis · Mathematics 2014-05-27 Arnoldo Bezanilla Lopez , Omar Leon Sanchez

We prove the following statement. Let $f\in\mathbb{R}[x_1,\ldots,x_d]$, for some $d\ge 3$, and assume that $f$ depends non-trivially in each of $x_1,\ldots,x_d$. Then one of the following holds. (i) For every finite sets…

Combinatorics · Mathematics 2018-07-09 Orit E. Raz , Zvi Shem Tov

Quaternionic Clifford analysis is a recent new branch of Clifford analysis, a higher dimensional function theory which refines harmonic analysis and generalizes to higher dimension the theory of holomorphic functions in the complex plane.…

Complex Variables · Mathematics 2016-04-07 Fred Brackx , Hennie De Schepper , David Eelbode , Roman Lavicka , Vladimir Soucek

We develop a new algorithm for factoring a bivariate polynomial $F\in \mathbb{K}[x,y]$ which takes fully advantage of the geometry of the Newton polygon of $F$. Under a non degeneracy hypothesis, the complexity is…

Commutative Algebra · Mathematics 2025-01-13 Martin Weimann

In this note we prove that the factorization theorem for dominated polynomials previously proved by the authors is equivalent to an alternative factorization scheme that uses classical linear techniques and a linearization process. However,…

Functional Analysis · Mathematics 2008-12-09 Geraldo Botelho , Daniel Pellegrino , Pilar Rueda

For any polynomial $P \in \mathbb{C}[X_1,X_2,...,X_n]$, we describe a $\mathbb{C}$-vector space $F(P)$ of solutions of a linear system of equations coming from some algebraic partial differential equations such that the dimension of $F(P)$…

Algebraic Geometry · Mathematics 2008-04-02 Hani Shaker

We derive the Taylor polynomial of a function, which is $m$-times continuously differentiable and positive homogeneous of order $m$. The Taylor polynomial in $a$ for $f(b)$ of order $m$ in general is a polynomial of order $m$ in $b-a$. If…

General Mathematics · Mathematics 2024-04-24 Joachim Paulusch , Sebastian Schlütter

The main objective of this paper is to introduce an algorithm for solving fractional and classical differential equations based on a new generalized fractional power series. The algorithm relies on expanding the solution of an FDE or an ODE…

General Mathematics · Mathematics 2024-06-26 Youness Assebbane , Mohamed Echchehira , Mohamed Bouaouid , Mustapha Atraoui

We establish a new generalized Taylor's formula for power fractional derivatives with nonsingular and nonlocal kernels, which includes many known Taylor's formulas in the literature. Moreover, as a consequence, we obtain a general version…

Spectral Theory · Mathematics 2024-01-29 Hanaa Zitane , Delfim F. M. Torres

In this paper, we consider Dunkl theory on R^d associated to a finite reflection group. This theory generalizes classical Fourier anal- ysis. First, we give for 1 < p <= 2, sufficient conditions for weighted Lp-estimates of the Dunkl…

Analysis of PDEs · Mathematics 2012-08-27 Chokri Abdelkefi , Faten Rached

This paper addresses an investigation on a factorization method for difference equations. It is proved that some classes of second order linear difference operators, acting in Hilbert spaces, can be factorized using a pair of mutually…

Mathematical Physics · Physics 2017-09-25 Alina Dobrogowska , Mahouton Norbert Hounkonnou

This paper contains a re-evaluation of the spectral approach and factorizability for regular matrix polynomials. In addition, solvent theory is extended from the monic and comonic cases to the regular case. The classification of extended…

Spectral Theory · Mathematics 2013-12-24 Nir Cohen , Edgar Pereira

We introduce the so-called Clifford-Gegenbauer polynomials in the framework of Dunkl operators, as well on the unit ball B(1), as on the Euclidean space $R^m$. In both cases we obtain several properties of these polynomials, such as a…

Classical Analysis and ODEs · Mathematics 2010-03-09 H. De Bie , N. De Schepper

A recently introduced nonlinear Fokker-Planck equation, derived directly from a master equation, comes out as a very general tool to describe phenomenologically systems presenting complex behavior, like anomalous diffusion, in the presence…

Statistical Mechanics · Physics 2009-11-13 Veit Schwammle , Evaldo M. F. Curado , Fernando D. Nobre

We generalize recent matrix-based factorization theorems for Lambert series generating functions generating the coefficients $(f \ast 1)(n)$ for some arithmetic function $f$. Our new factorization theorems provide analogs to these…

Number Theory · Mathematics 2019-09-23 Hamed Mousavi , Maxie D. Schmidt

We present an elementary proof of a general version of Montel's theorem in several variables which is based on the use of tensor product polynomial interpolation. We also prove a Montel-Popoviciu's type theorem for functions…

Classical Analysis and ODEs · Mathematics 2014-07-03 A. G. Aksoy , J. M. Almira

Factorization theorem plays the central role at high energy colliders to study standard model and beyond standard model physics. The proof of factorization theorem is given by Collins, Soper and Sterman to all orders in perturbation theory…

High Energy Physics - Phenomenology · Physics 2010-05-28 Gouranga C Nayak

We extend the Reed Dawson identity for Knuth's old sum with a complex parameter, and we offer two separate hypergeometric series-based proofs of this generalization, and we apply this generalization to introduce binomial-harmonic sum…

Combinatorics · Mathematics 2022-05-13 Arjun K. Rathie , John M. Campbell