Related papers: Global algebraic linear differential operators

On filtered manifolds one can define a different notion of order for the differential operators. In this paper, we use generalized fixed point algebras to construct a pseudodifferential extension that reflects this behaviour. In the…

The local $L^2$-mapping property of Fourier integral operators has been established in H\"ormander \cite{H} and in Eskin \cite{E}. In this paper, we treat the global $L^2$-boundedness for a class of operators that appears naturally in many…

Let $A(D)$ be an elliptic homogeneous linear differential operator of order $\nu$ on $\mathbb{R}^{N}$, $N \geq 2$, from a complex vector space E to a complex vector space F. In this paper we show that if $\ell\in \mathbb{R}$ satisfies $0<…

Let $X$ be a nonsingular variety defined over an algebraically closed field of characteristic $0$, and $D$ be a free divisor. We study the motivic Chern class of $D$ in the Grothendieck group of coherent sheaves $G_0(X)$, and another class…

We discuss the essential spectrum of essentially self-adjoint elliptic differential operators of first order and of Laplace type operators on Riemannian vector bundles over geometrically finite orbifolds.

This paper is the first of two papers constructing a calculus of pseudodifferential operators suitable for doing analysis on Q-rank 1 locally symmetric spaces and Riemannian manifolds generalizing these. This generalization is the interior…

We derive global gradient estimates for $W^{1,p}_0(\Omega)$-weak solutions to quasilinear elliptic equations of the form $$ \mathrm{div\,}\mathbf{a}(x,u,Du)=\mathrm{div\,}(|F|^{p-2}F) $$ over $n$-dimensional Reifenberg flat domains. The…

Let $\Omega\subset\mathbb{R}^n, n\geq 2$, be an open set. For an elliptic differential operator $L$ on $\Omega$ with real analytic coefficients and a point $p\in\Omega$, we construct a smooth function $g$ with the following properties: $g$…

In differential geometry, the notation d^n f along with the corresponding formalism has fallen into disuse since the birth of exterior calculus. However, differentials of higher order are useful objects that can be interpreted in terms of…

We prove a Harnack inequality for distributional solutions to a type of degenerate elliptic PDEs in $N$ dimensions. The differential operators in question are related to the Kolmogorov operator, made up of the Laplacian in the last $N-1$…

{We explore a simple {\it geometric model} for functions between spaces of the same dimension (in infinite dimensions, we require that Jacobians be Fredholm operators of index zero). The model combines standard results in analysis and…

In this paper, we consider an elliptic operator obtained as the superposition of a classical second-order differential operator and a nonlocal operator of fractional type. Though the methods that we develop are quite general, for…

In this paper we study in detail algebraic properties of the algebra $\mathcal D(W)$ of differential operators associated to a matrix weight of Gegenbauer type. We prove that two second order operators generate the algebra, indeed $\mathcal…

We observe that for a large class of non-amenable groups $G$, one can find bounded representations of $A(G)$ on Hilbert space which are not completely bounded. We also consider restriction algebras obtained from $A(G)$, equipped with the…

Let G be a connected compact Lie group acting on a manifold M and let D be a transversally elliptic operator on M. The multiplicity of the index of D is a function on the set of irreducible representations of G. Let T be a maximal torus of…

We show that almost all the linear differential operators factors obtained in the analysis of the n-particle contribution of the susceptibility of the Ising model for $\, n \le 6$, are operators "associated with elliptic curves". Beyond the…

Given two real numbers, the $L^2$ functions whose Fourier transforms vanish with a certain rapidity near the given numbers are characterised as those that are expressible as the sum of a certain number of generalised finite differences that…

For ring of differential operators on smooth affine algebraic variety over perfect field of prime characteristic a set of algebra generators and a set of defining relations are found explicitly.

We give a complete classification of conformally covariant differential operators between the spaces of differential $i$-forms on the sphere $S^n$ and $j$-forms on the totally geodesic hypersphere $S^{n-1}$ by analyzing the restriction of…

There is a class of Laplacian like conformally invariant differential operators on differential forms $L^\ell_k$ which may be considered the generalisation to differential forms of the conformally invariant powers of the Laplacian known as…