Related papers: Differential operators on equivariant vector bundl…

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…

Let E be an operator algebra on a Hilbert space with finite-dimensional generated C*-algebra. A classification is given of the locally finite algebras and the operator algebras obtained as limits of direct sums of matrix algebras over E…

The Branson-Gover operators are conformally invariant differential operators of even degree acting on differential forms. They can be interpolated by a holomorphic family of conformally invariant integral operators called fractional…

Let $\Delta$ be a linear differential operator acting on the space of densities of a given weight $\lo$ on a manifold $M$. One can consider a pencil of operators $\hPi(\Delta)=\{\Delta_\l\}$ passing through the operator $\Delta$ such that…

A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a…

In this paper, we study scalar the forth order linear differential operators over an oriented 2-dimensional manifold. We investigate differential invariants of these operators and show their application to the equivalence problem.

We conjecture a geometrical form of the Paley-Wiener theorem for the Dunkl transform and prove three instances thereof, one of which involves a limit transition from Opdam's results for the graded Hecke algebra. Furthermore, the connection…

In this paper we study closed subspaces of ultradifferentiable functions which are invariant under the differentiation operator. We propose a version of spectral synthesis which takes into account the presence of non-trivial differentiation…

Using the method of similar operators we study an even order differential operator with periodic, semiperiodic, and Dirichlet boundary conditions. We obtain asymptotic formulas for eigenvalues of this operator and estimates for its spectral…

We prove that the Casimir operator acting on sections of a homogeneous vector bundle over a generalized flag manifold naturally extends to an invariant differential operator on arbitrary parabolic geometries. We study some properties of the…

There has been a long-standing conjecture in Banach algebra that every amenable operator is similar to a normal operator. In this paper, we study the structure of amenable operators on Hilbert spaces. At first, we show that the conjecture…

A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis (the generalized Bochner problem) is given. The main result is that any operator with…

On conformal manifolds of even dimension $n\geq 4$ we construct a family of new conformally invariant differential complexes. Each bundle in each of these complexes appears either in the de Rham complex or in its dual. Each of the new…

Differential operators usually result in derivatives expressed as a ratio of differentials. For all but the simplest derivatives, these ratios are typically not algebraically manipulable, but must be held together as a unit in order to…

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 indicate smooth real commuting matrix differential operators whose eigenvalues and eigenfunctions are parametrized by two-dimensional principally polarized abelian varieties.

Some properties and relations satisfied by the polynomial solutions of the bispectral problem are studied. Given a differential operator, under certain restrictions its polynomial eigenfunctions are explicitly obtained, as well as the…

In this expository article, we consider first order elliptic differential operators acting on smooth vector bundles over compact manifolds, and certain invariants derived from the analysis of these operators, namely the eta invariant} and…

Let $f$ be a symmetric norm on ${\mathbb R}^n$ and let ${\mathcal B}({\mathcal H})$ be the set of all bounded linear operators on a Hilbert space ${\mathcal H}$ of dimension at least $n$. Define a norm on ${\mathcal B}({\mathcal H})$ by…

In this paper, we investigate the spectrum of the self adjoint differential operator with operator coefficitent in a separable Hilbert space. We also derive asymptotic formulas for the sum of eigenvalues of this operator.