Related papers: Fiber-Wise Linear Differential Operators

We give a computationally efficient method for constructing the linear differential operator with polynomial coefficients whose space of holomorphic solutions is spanned by all the branches of a function defined by a generic algebraic…

Any leafwise connection on a fibre bundle over a foliated manifold is proved to come from a connection on this fibre bundle.

In this paper, we study Lie superalgebras of $2\times 2$ matrix-valued first-order differential operators on the complex line. We first completely classify all such superalgebras of finite dimension. Among the finite-dimensional…

We study the structure of the fibre operators corresponding to periodic magnetic pseudo-differential operators having periodic magnetic potentials. We obtain explicit formulas for their distribution kernel, both when these fibres are seen…

The linear operators defined on the Lipschitz projective tensor product of X and E motivate the study of a distinct class of operators acting on the cartesian produc X E. This class, denoted by LipL(X E;F), combines Lipschitz and linear…

This work is the first in a series of papers that, among other things, extends the formalism of diolic differential calculus, wherein a new context for obtaining differential calculus in vector bundles was established. Here we provide a…

This paper grew out of the author's work on arXiv:2504.18460. Differential operators in the sense of Grothendieck acting between modules over a commutative ring can be interpreted as torsion elements in the bimodule of all operators with…

We show that the category of affine bundles over a smooth manifold M is equivalent to the category of affine spaces modelled on projective finitely generated C^\infty(M)-modules. Using this equivalence of categories, we are able to give an…

For a projective variety $X$ and a line bundle $L$ over $X$, one considers the $L-$twisted global differential operator algebra $\call{D}_L(X)$ which naturally operates on the space of global sections $H^0(X,L)$. In the case where $X$ is…

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…

Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance…

A symbolic calculus for a pseudo-differential operators acting on sections of a homogeneous vector bundle over a compact homogeneous space $G/H$ with compact $G$ and $H$ is developed. We realize the symbol of a pseudo-differential operator…

This paper deals with well-known higher-order generalizations of Hankel operators. We show that higher-order Hankel operators can be written explicitly as linear differential operators, and give the exact form of these differential…

Bol operators (Bols for short) are differential operators invariant under the projective action of $\mathfrak{pgl}(2)\simeq\mathfrak{sl}(2)$ between spaces of weighted densities on the 1-dimensional manifold. Here, we described analogs of…

Any bounded linear operator $ T $ on $ L^2(\mathbb{R}^n) $ gives rise to the operator $ S= B \circ T \circ B^\ast $ on the Fock space $ \mathcal{F}(\C^n) $ where $ B $ is the Bargmann transform. In this article we identify those $ S $ which…

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…

We establish some properties of the ring of differential operators on the quantized flag manifold. Especially, we give an explicit description of its localization on an affine open subset in terms of the quantum Weyl algebra ($q$-analogue…

In this paper we derive structure theorems that characterize the spaces of linear and non-linear differential operators that preserve finite dimensional subspaces generated by polynomials in one or several variables. By means of the useful…

A VB-algebroid is a vector bundle object in the category of Lie algebroids. We attach to every VB-algebroid a differential graded Lie algebra and we show that it controls deformations of the VB-algebroid structure. Several examples and…

Differential operators on Schwartz distributions conventionally are defined as the transpose of differential operators on functions with compact support. They do not exhaust all differential operators. We follow algebraic formalism of…