Related papers: Multiple Factorizations of Bivariate Linear Partia…
We develop and compare two algorithms for computing first-order right-hand factors in the ring of linear Mahler operators$\ell_r M^r + \dots + \ell_1 M + \ell_0$where $\ell_0, \dots, \ell_r$ are polynomials in~$x$ and $Mx = x^b M$ for some…
In this paper we investigate factorizations of polynomials over the ring of dual quaternions into linear factors. While earlier results assume that the norm polynomial is real ("motion polynomials"), we only require the absence of real…
We study {\it non-holonomic} overideals of a left differential ideal $J\subset F[\partial_x, \partial_y]$ in two variables where $F$ is a differentially closed field of characteristic zero. The main result states that a principal ideal $J=<…
Following the works by Lin et al. (Circuits Syst. Signal Process. 20(6): 601-618, 2001) and Liu et al. (Circuits Syst. Signal Process. 30(3): 553-566, 2011), we investigate how to factorize a class of multivariate polynomial matrices. The…
We investigate two types of boundedness criteria for bilinear Fourier multiplier operators with symbols with bounded partial derivatives of all (or sufficiently many) orders. Theorems of the first type explicitly prescribe only a certain…
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…
A factorization theory is proposed for Wiener-Hopf plus Hankel operators with almost periodic Fourier symbols. We introduce a factorization concept for the almost periodic Fourier symbols such that the properties of the factors will allow…
We consider the classical factorization problem of a third order ordinary differential operator $L-\lambda$, for a spectral parameter $\lambda$. It is assumed that $L$ is an algebro-geometric operator, that it has a nontrivial centralizer,…
We will show a local solvability result for a class of degenerate second order linear partial differential operators with a complex subprincipal symbol. Due to the form of the operators in the class the subprincipal symbol is invariantly…
A well-known theorem factors a scalar coefficient differential operator given a linearly independent set of functions in its kernel. The goal of this paper is to generalize this useful result to other types of operators. In place of the…
We propose a generalization of Laplace transformations to the case of linear partial differential operators (LPDOs) of arbitrary order in R^n. Practically all previously proposed differential transformations of LPDOs are particular cases of…
In this paper we describe three different variations of prime ideals: strongly irreducible ideals, strongly prime ideals and insulated prime ideals in the context of Leavitt path algebras. We give necessary and sufficient conditions under…
We present an algorithm to compute $\mathrm{LCLM}$-decompositions for linear differentials operators with coefficients in the rational function field of characteristic $p$, $\mathbb{F}_{p^n}(t)$. We show that for an operator $L$ of order…
Motion polynomials (polynomials over the dual quaternions with nonzero real norm) describe rational motions. We present a necessary and sufficient condition for reduced bounded motion polynomials to admit factorizations into monic linear…
If the $n-th$ order differential equation is not exact, under certain conditions, an integrating factor exists which transforms the differential equation into an exact one. Hence, its order can be reduced to the lower order. In this paper,…
We explore the existence of a class of generalised Laplace maps for third order partial differential operators of the form…
Our main contributions can be divided in three parts: (1) Fixpoint extensions of first-order logic: we give a precise syntactic and semantic characterization of the relationship between $\mathrm{FO(TC^1)}$ and $\mathrm{FO(LFP)}$; (2)…
We consider the semiconjugate factorization and reduction of order for non-autonomous, nonlinear, higher order difference equations containing linear arguments. These equations have appeared in several mathematical models in biology and…
We investigate the application of windowed Fourier frames (WFFs) to the numerical solution of partial differential equations, focussing on elliptic equations. The action of a partial differential operator (PDO) on a windowed plane wave is…
Recently, \cite{Cao:2025hio} demonstrated the $2$-split for form factor under specific kinematic constraints. This factorization is analogous to that observed in scattering amplitudes. A key consequence of this structure is the presence of…