Related papers: A note on invariant differential operators on Sieg…
We construct new families of conformally invariant differential operators acting on densities. We introduce a simple, direct approach which shows that all such operators arise via this construction when the degree is bounded by the…
This paper is devoted to the study of some connections between coadjoint orbits in infinite dimensional Lie algebras, isospectral deformations and linearization of dynamical systems. We explain how results from deformation theory,…
In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebra $so^*(12)$. We give the main multiplets of indecomposable elementary representations. Due…
We study the phenomena that arise when we combine the standard pseudodifferential operators with those operators that appear in the study of some sub-elliptic estimates, and on strongly pseudoconvex domains. The algebra of operators we…
In this paper we study a class of Jacobi operators, such that each operator is generated by the unit Borel measure with a support consisting of a finite number of intervals on the real line R and a finite number of points in C, located…
We first study some properties of images of commuting differential operators of polynomial algebras of order one with constant leading coefficients. We then propose what we call the image conjecture on these differential operators and show…
We introduce a new class of natural, explicitly defined, transversally elliptic differential operators over manifolds with compact group actions. Under certain assumptions, the symbols of these operators generate all the possible values of…
We consider symmetric second-order differential operators with real coefficients such that the corresponding differential equation is in the limit circle case at infinity. Our goal is to construct the theory of self-adjoint realizations of…
Functional determinants of differential operators play a prominent role in theoretical and mathematical physics, and in particular in quantum field theory. They are, however, difficult to compute in non-trivial cases. For one dimensional…
We characterize Riemannian manifolds of constant sectional curvature in terms of commutation properties of their Jacobi operators.
The article is devoted to the investigation of operators on a non locally compact group algebra. Their isomorphisms are also studied.
We study a pair of commuting difference operators arising from the elliptic C_2^{(1)}-face model. The operators, whose coefficients are expressed in terms of the Jacobi's elliptic theta function, act on the space of meromorphic functions on…
In this paper, we introduce and study non-local Jacobi operators, which generalize the classical (local) Jacobi operators. We show that these operators extend to generators of ergodic Markov semigroups with unique invariant probability…
The equivalence problem for linear differential operators of the second order, acting in vector bundles, is discussed. The field of rational invariants of symbols is described and connections, naturally accosiated with differential…
We give explicit descriptions of rings of differential operators of toric face rings in characteristic $0$. For quotients of normal affine semigroup rings by radical monomial ideals, we also identify which of their differential operators…
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…
This paper introduces a notion of gradient and an infimal-convolution operator that extend properties of solutions of Hamilton Jacobi equations to more general spaces, in particular to graphs. As a main application, the hypercontractivity…
Symmetry is present in many tasks in computer vision, where the same class of objects can appear transformed, e.g. rotated due to different camera orientations, or scaled due to perspective. The knowledge of such symmetries in data coupled…
We define, in a consistent way, non-local pseudo-differential operators acting on a space of analytic functionals. These operators include the fractional derivative case. In this context we show how to solve homogeneous and inhomogeneous…
New concept of conditional differential invariant is discussed that would allow description of equations invariant with respect to an operator under a certain condition. Example of conditional invariants of the projective operator is…