Related papers: Symmetry breaking differential operators, the sour…
We compute arithmetic support of the formal deformations $D=P+tQ_1+t^2Q_2+...$ of the differential operator $P=(x\partial_x-r_1)...(x\partial_x-r_k)$, where $r_1,...,r_k\in\mathbb{Q}$ for sufficiently large primes $p$ in terms of the…
The study of symmetries of partial differential equations (PDEs) has been traditionally treated as a geometrical problem. Although geometrical methods have been proven effective with regard to finding infinitesimal symmetry transformations,…
Jordan operator algebras are norm-closed spaces of operators on a Hilbert space with a^2 in A for all a in A. In two recent papers by the authors and Neal, a theory for these spaces was developed. It was shown there that much of the theory…
If $a$ is a densely defined sectorial form in a Hilbert space which is possibly not closable, then we associate in a natural way a holomorphic semigroup generator with $a$. This allows us to remove in several theorems of semigroup theory…
We provide an explicit set of algebraically independent generators for the algebra of invariant differential operators on the Riemannian symmetric space associated with $\SL_n(\R)$.
We systematically introduce the idea of applying differential operator method to find a particular solution of an ordinary nonhomogeneous linear differential equation with constant coefficients when the nonhomogeneous term is a polynomial…
Let $D:\Omega\xrightarrow{}\Omega$ be a differential operator defined in the exterior algebra $\Omega$ of differential forms over the polynomial ring $S$ in $n$ variables. In this work we give conditions for deforming the module structure…
We present a new construction for the Hodge operator for differential manifolds based on a Fourier (Berezin)-integral representation. We find a simple formula for the Hodge dual of the wedge product of differential forms, using the…
Recently a new formalism for perturbations of Maxwell's equations on the background of the Kerr-NUT-(A)dS spacetime was proposed, with which the equations are reduced to a equation of motion of a scalar field that can be solved by…
We study the algebra of invariant differential operators on a certain homogeneous vector bundle over a Riemannian symmetric space of type $A_2$. We computed radial parts of its generators explicitly to obtain matrix-valued commuting…
I explore several related routes to deriving the Jordan-algebraic structure of finite-dimensional quantum theory from more transparent operational or physical principles, mainly involving ideas about the symmetries of, and the correlations…
We provide some insights in the study of branching problems of reductive groups, and a method of investigations into symmetry breaking operators. First, we give geometric criteria for finiteness property of linearly independent continuous…
In this paper we determine all possible cohomological invariants of Aut(J)-torsors in Galois cohomology with mod 2 coefficients (characteristic of the base field not 2), for J a split central simple Jordan algebra of odd degree n>=3. This…
We investigate a new representation of general operators by means of sums of shifted Gabor multipliers. These representations arise by studying the matrix of an operator with respect to a Gabor frame. Each shifted Gabor multiplier…
In this article, we investigate differential operators on the Siegel-Jacobi space that are invariant under the natural action of the Jacobi group. These invariant differential operators play an important role in the arithmetic theory of…
Axial algebras are commutative nonassociative algebras generated by a finite set of primitive idempotents which action on an algebra is semisimple, and the fusion laws on the products between eigenvectors for these idempotents are…
The purpose of this paper is to show that the mathematical treatment of three dimensional rotations can be simplified, and its geometrical understanding improved, by using the Rodrigues' vector representation. We present a novel geometrical…
The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. All possible reductions of these equations to…
Operator splitting methods allow to split the operator describing a complex dynamical system into a sequence of simpler subsystems and treat each part independently. In the modeling of dynamical problems, systems of (possibly coupled)…
The Hi-Jack symmetric polynomials, which are associated with the simultaneous eigenstates for the first and second conserved operators of the quantum Calogero model, are studied. Using the algebraic properties of the Dunkl operators for the…