Related papers: Remarks on natural differential operators with ten…

Natural linear and coalgebra transformations of tensor algebras are studied. The representations of certain combinatorial groups are given. These representations are connected to natural transformations of tensor algebras and to the groups…

In resonance to a recent geometric framework proposed by Douglas and Yang, a functional model for certain linear bounded operators with rank-one self-commutator acting on a Hilbert space is developed. By taking advantage of the refined…

We study cone differential operators on the half-axis and edge-degenerate differential operators on a half-space. We construct subspaces of edge Sobolev spaces that can be considered as natural domains for edge-degenerate operators and…

We define a class of discrete operators that, in particular, include the delta and nabla fractional operators.

We give an algorithm to write down all conformally invariant differential operators acting between scalar functions on Minkowski space. All operators of order k are nonlinear and are functions on a finite family of functionally independent…

This is the second half of a two-part series studying tensor categories of unitary vertex operator algebras from a unitary point of view.

Differentiations of operator algebras over non-archimedean spherically complete fields are investigated. Theorems about a differentiation being internal are demonstrated.

We give a few observations on different types of bounded operators on a topological vector space X and their relations with compact operators on X. In particular, we investigate when these bounded operators coincide with compact operators.…

Using simultaneously two operator identities, we consider the inversion of the convolution operators on a rectangular. The structure of the inverse operators and of some corresponding forms, which are important in signal processing, is…

There is a relatively well-known description of the algebra of (higher order) left differential operators on commutative algebras. This note gives a construction of similar flavor for algebras of differential operators on not necessarily…

A derived operation is a bilinear operation on a commutative associative algebra $A$ defined intrinsically out of its product and several derivations of the product. We show that operators of left (or right) multiplications of a derived…

We generalize reduction theorems for classical connections to operators with values in $k$-th order natural bundles. Using the first reduction theorem in order two we classify all (0,2)-tensor fields on the cotangent bundle of a manifold…

We give a complete classification of tangential bidifferential operators of total order at most $n$ which are expressed purely in terms of the Laplacian on the ambient space of an $n$-dimensional manifold. This gives a curved analogue of…

We generalize the definition of convolution of vectors and tensors on the 2-sphere, and prove that it commutes with differential operators. Moreover, vectors and tensors that are normal/tangent to the spherical surface remain so after the…

We study some basic properties of the class of universal operators on Hilbert space, and provide new examples of universal operators and universal pairs.

For a large class of integral operators or second order differential operators, their isospectral (or cospectral) operators are constructed explicitly in terms of $h$-transform (duality). This provides us a simple way to extend the known…

We develop a systematic way for constructing bispectral algebras of commuting ordinary differential operators of any rank $N$. It combines and unifies the ideas of Duistermaat-Gr\"unbaum and Wilson. Our construction is completely…

Invariant operator-valued tensor fields on Lie groups are considered. These define classical tensor fields on Lie groups by evaluating them on a quantum state. This particular construction, applied on the local unitary group U(n)xU(n), may…

A complete classification of linear differential operators possessing finite-dimensional invariant subspace with a basis of monomials is presented.

It was recently conjectured that every system of exceptional orthogonal polynomials is related to classical orthogonal polynomials by a sequence of Darboux transformations. In this paper we prove this conjecture, which paves the road to a…