Related papers: Divided difference operators on polytopes
We study $\mathcal{O}$-operators of associative conformal algebras with respect to conformal bimodules. As natural generalizations of $\mathcal{O}$-operators and dendriform conformal algebras, we introduce the notions of twisted Rota-Baxter…
This paper is dedicated to finding the quadrature operator eigenstates and wavefunctions of the most general $f$-deformed oscillators. A definition for quadrature operator for deformed algebra is derived to obtain the quadrature operator…
In this paper, we introduce the concept of operator arithmetic-geometrically convex functions for positive linear operators and prove some Hermite-Hadamard type inequalities for these functions. As applications, we obtain trace inequalities…
Using {\it weighted traces} which are linear functionals of the type $$A\to tr^Q(A):=(tr(A Q^{-z})-z^{-1} tr(A Q^{-z}))_{z=0}$$ defined on the whole algebra of (classical) pseudo-differential operators (P.D.O.s) and where $Q$ is some…
We study invariant operators in general tensor models. We show that representation theory provides an efficient framework to count and classify invariants in tensor models. In continuation and completion of our earlier work, we present two…
We extend to manifolds endowed with a general geometric structure, the classical notions of gradient as well as Laplace operator, and provide some of their natural properties.
In this chapter, the Hilbert space framework in the mathematical theory of composite materials is introduced for studying the properties of effective operators. The goal is to introduce some of the key concepts and fundamental theorems in…
It is shown that a covariant derivative on any d-dimensional manifold M can be mapped to a set of d operators acting on the space of functions on the principal Spin(d)-bundle over M. In other words, any d-dimensional manifold can be…
The problem of a differential operator left- and right division is solved in terms of generalized Bell polinomials for nonabelian differential unitary ring. The definition of the polinomials is made by means of recurrent relations. The…
The aim of the present paper is to define compact operators on asymmetric normed spaces and to study some of their properties. The dual of a bounded linear operator is defined and a Schauder type theorem is proved within this framework. The…
We first study some properties of images of commuting differential operators of polynomial algebras of order one with constant leading coefficients. We then propose what we call the image conjecture on these differential operators and show…
We study multiplicative systems of linear mappings acting on the toy Fock space, a.k.a.\ Rademacher chaos or Walsh-Fourier series, related to the creation, annihilation, and conservation operators in quantum probability. Like differential…
A new algorithm for the efficient numerical approximation of weakly singular integrals over convex polytopes is introduced. Such integrals appear in the Galerkin discretizations of integral equations and nonlocal partial differential…
Centered weighted composition operators on $L^2$-spaces are characterized. The characterization is obtained without the assumption that the operator is a product of a multiplication and a composition operator. The concept of spectrally…
We consider differential operators acting on densities of arbitrary weights on manifold $M$ identifying pencils of such operators with operators on algebra of densities of all weights. This algebra can be identified with the special…
We consider a natural basis of the Iwahori fixed vectors in the Whittaker model of an unramified principal series representation of a split semisimple p- adic group, indexed by the Weyl group. We show that the elements of this basis may be…
Geometry arising from two diffusion operators (smooth semi-elliptic, second order differential operators) on different spaces but intertwined by a smooth map is described. Particular cases arise from Riemannian submersions when the…
We present a general scheme to derive lattice differential operators from the discrete velocities and associated Maxwell-Boltzmann distributions used in lattice hydrodynamics. Such discretizations offer built-in isotropy and recursive…
We will introduce an operation "twisting" on Hochschild complex by analogy with Drinfeld's twisting operations. By using the twisting and derived bracket construction, we will study differential graded Lie algebra structures associated with…
Let $M$ be a compact Riemannian manifold endowed with an isometric action of a compact Lie group. The method of the Witten deformation is used to compute the virtual representation-valued equivariant index of a transversally elliptic, first…