Related papers: Differential Operators on the free algebras
We study relationships between spinor representations of certain Lie algebras and Lie superalgebras of differential operators on the circle and values of $\zeta$--functions at the negative integers. By using formal calculus techniques we…
In this paper we introduce a notion of duality for matrix valued orthogonal polynomials with respect to a measure supported on the nonnegative integers. We show that the dual families are closely related to certain difference operators…
In this note we study algebras of chiral differential operators over an algebraic group and over homogeneous spaces $G/G'$ where $G$ is simple and $G'$ is unipotent or parabolic.
This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in…
We describe the construction of the quantum deformed affine Lie algebras using the vertex operators in the free field theory. We prove the Serre relations for the quantum deformed Borel subalgebras of affine algebras, namely the case of…
We define the concept of completely regular ordinary differential operators and give various criteria for operators to belong to this class. We give also criteria for Birkhof regularity of ordinary differential operators in terms of the…
In this paper, we consider the $L^2$-boundedness of pseudo-differential operators with symbols in $\alpha$-modulation spaces.
Fix a manifold M, and let V be an infinite dimensional Lie algebra of vector fields on M. Assume that V contains a finite dimensional semisimple maximal subalgebra A, the projective or conformal subalgebra. A projective or conformal…
Differential graded (DG) algebras are powerful tools from rational homotopy theory. We survey some recent applications of these in the realm of homological commutative algebra.
We give the description of homogeneous Rota-Baxter operators, Reynolds operators, Nijenhuis operators, Average operators and differential operator of weight 1 of null-filiform associative algebras of arbitrary dimension.
In this paper we investigate the spectrum of the differential operators generated by the ordinary differential expression of odd order with PT-symmertic periodic matrix coefficients
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…
Let $\Delta^{(\alpha)}$ denote the fractional difference operator. In this paper, we define new difference sequence spaces $c_0(\Gamma,\Delta^{(\alpha)},u)$ and $c(\Gamma,\Delta^{(\alpha)},u)$. Also, the $\beta-$ dual of the spaces…
We introduce certain correlation functions (graded $q$--traces) associated to vertex operator algebras and superalgebras which we refer to as $n$--point functions. These naturally arise in the studies of representations of Lie algebras of…
Results of our previous note, "Gerbes of chiral differential operators" (Math. Res. Letters, 7(2000), 55-66), are discussed in the algebraic category.
In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…
We solve the following problem: to describe in geometric terms all differential operators of the second order with a given principal symbol. Initially the operators act on scalar functions. Operator pencils acting on densities of arbitrary…
For ring of differential operators on smooth affine algebraic variety over perfect field of prime characteristic a set of algebra generators and a set of defining relations are found explicitly.
We study natural differential operators transforming two tensor fields into a tensor field. First, it is proved that all bilinear operators are of order one, and then we give the full classification of such operators in several concrete…
A notion of Cartan pairs as an analogy of vector fields in the realm of noncommutative geometry has been proposed in q-alg/9609011 In this paper we give an outline of the construction of a noncommutative analogy of the algebra of partial…