Related papers: Differential Calculus on h-Deformed Spaces
A generalization of differential operators are pseudodifferential operators which are used for reasoning about partial differential equations with variable coefficients. A lot of useful properties about classical pseudodifferential…
For an operator generating a group on $L^p$ spaces transference results give bounds on the Phillips functional calculus also known as spectral multiplier estimates. In this paper we consider specific group generators which are abstraction…
Given a complex, separable Hilbert space $\mathcal{H}$, we characterize those operators for which $\| P T (I-P) \| = \| (I-P) T P \|$ for all orthogonal projections $P$ on $\mathcal{H}$. When $\mathcal{H}$ is finite-dimensional, we also…
We investigate the algebro-geometric structure of a novel two-parameter quantum deformation which exhibits the nature of a semidirect or cross-product algebra built upon GL(2) x GL(1), and is related to several other known examples of…
We construct an algebra of pseudodifferential operators on each groupoid in a class that generalizes differentiable groupoids to allow manifolds with corners. We show that this construction encompasses many examples. The subalgebra of…
We solve the following problem: to describe in geometric terms all differential operators of the second order with a given principal symbol. Initially the operators act on scalar functions. Operator pencils acting on densities of arbitrary…
We give an alternative proof of the general chain rule for functions of bounded variation ([ADM90]), which allows to compute the distributional differential of $\varphi\circ F$, where $\varphi\in \mathrm{LIP}(\mathbb{R}^m)$ and…
The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed in recent work (collaboration with H.…
In this paper differential operators on various moduli spaces (e.g. of holomorphic vector bundles) are described in a canonical way in terms of the geometry of a certain distinguished completion of an appropriate configuration space.
We obtain a global resolution for the sheaf of differential operators on smooth geometric quotients of free linear actions of algebraic groups. The terms of our resolution involve symmetric and alternating powers of vector bundles easily…
In this paper we solve some differential equations in the $D_h$ derivative in Ward's sense. We use a special metric in the formal power series ring $\K[[x]]$. The solutions of that equations are giving in terms of fixed points for certain…
We introduce a new formalism of differential operators for a general associative algebra A. It replaces Grothendieck's notion of differential operator on a commutative algebra in such a way that derivations of the commutative algebra are…
Discrete mathematics, the study of finite structures, is one of the fastest growing areas in mathematics and optimization. Discrete fractional calculus (DFC) theory that is an important subject of the fractional calculus includes the…
We study certain classes of equations for $F_q$-linear functions, which are the natural function field counterparts of linear ordinary differential equations. It is shown that, in contrast to both classical and $p$-adic cases, formal power…
We introduce new concepts in order to develop a general formalism for twisted differential operators in several variables. We investigate the notion of twisted coordinates on Huber rings that allows us to build various rings of twisted…
We obtain a family of functional identities satisfied by vector-valued functions of two variables and their geometric inversions. For this we introduce particular differential operators of arbitrary order attached to Gegenbauer polynomials.…
We classify subalgebras of a ring of differential operators which are big in the sense that the extension of associated graded rings is finite. We show that these subalgebras correspond, up to automorphisms, to uniformly ramified finite…
In this work, some generalizations and refinements inequalities for numerical radius of the product of Hilbert space operators are proved. New inequalities for numerical radius of block matrices of Hilbert space operators are also…
In this survey article we discuss the question: to what extent is an algebraic variety determined by its ring of differential operators? In the case of affine curves, this question leads to a variety of mathematical notions such as the Weyl…
We construct a cofibrantly generated model structure on the category of differential non-negatively graded quasi-coherent commutative $D_X$-algebras, where $D_X$ is the sheaf of differential operators of a smooth afine algebraic variety X.…