Related papers: Noetherian operators and primary decomposition
The present paper, is devoted to investigation of operator--valued Fourier multiplier theorems from $B_{q_{1},r}^{s}$ to $B_{q_{2},r}^{s}$, optimal embedding of Besov spaces, the separability and positivity of differential operators. Here,…
In this paper we describe the method which we applied to successfully compute the primary decomposition of a certain ideal coming from applications in combinatorial algebra and algebraic statistics regarding conditional independence…
There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial…
We propose a geometric framework to describe and analyze a wide array of operator splitting methods for solving monotone inclusion problems. The initial inclusion problem, which typically involves several operators combined through…
Let $X$ be a right Hilbert module over a $C^*$-algebra $A$ equipped with the canonical operator space structure. We define an elementary operator on $X$ as a map $\phi : X \to X$ for which there exists a finite number of elements $u_i$ in…
Rota-Baxter operators are an algebraic abstraction of integration. Following this classical connection, we study the relationship between Rota-Baxter operators and integrals in the case of the polynomial algebra $\mathbf{k}[x]$. We consider…
We define convex-geometric counterparts of divided difference (or Demazure) operators from the Schubert calculus and representation theory. These operators are used to construct inductively polytopes that capture Demazure characters of…
In this paper we show that for a large natural class of vertex operator algebras (VOAs) and their modules, the Zhu algebras and bimodules (and their $g$-twisted analogs) are Noetherian. These carry important information about the…
Neural operators serve as universal approximators for general continuous operators. In this paper, we derive the approximation rate of solution operators for the nonlinear parabolic partial differential equations (PDEs), contributing to the…
We construct bounded linear operators that map $H^1$ conforming Lagrange finite element spaces to $H^2$ conforming virtual element spaces in two and three dimensions. These operators are useful for the analysis of nonstandard finite element…
In the present paper, we aim to introduce the cohomology of $\mathcal{O}$-operators defined on the Hom-Lie conformal algebra concerning the given representation. To obtain the desired results, we describe three different cochain complexes…
This article gives a fundamental discussion on variable coefficients, self-adjoint, formally partially hypoelliptic differential operators. A generalization of the results to pseudo differential operators, is given in a following article in…
We systematically introduce the idea of applying differential operator method to find a particular solution of an ordinary nonhomogeneous linear differential equation with constant coefficients when the nonhomogeneous term is a polynomial…
It is known that local operators in quantum field theory transform in representations of ordinary global symmetry groups. The purpose of this paper is to generalise this statement to extended operators such as line and surface defects. We…
Of crucial importance to the development of quantum computing and information has been the construction of a quantum operations formalism that admits a description of quantum noise while simultaneously revealing the behavior of an open…
We introduce a new approach to the classification of operator identities, based on basic concepts from the theory of algebraic operads together with computational commutative algebra applied to determinantal ideals of matrices over…
We classify the primitive ideals of generalized down-up algebras
We study differential operators on an elliptic curve of order higher than 2 which are algebraically integrable (i.e., finite gap). We discuss classification of such operators of order 3 with one pole, discovering exotic operators on special…
In this paper, we give a generic algorithm of the transition operators between Hermitian Young projection operators corresponding to equivalent irreducible representations of SU(N), using the compact expressions of Hermitian Young…
We suppose that $G$ is a locally compact abelian group, $Y$ is a measure space, and $H$ is a reproducing kernel Hilbert space on $G\times Y$ such that $H$ is naturally embedded into $L^2(G\times Y)$ and it is invariant under the…