相关论文: Commuting differential operators with regular sing…

For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…

We derive the most general families of differential operators of first and second degree semi-commuting with the differential operators of the Heun class. Among these families we classify all those families commuting with the Heun class. In…

Before we proposed an algebraic technics for the Hamiltonian approach to the evolution systems of partial differential equations, including systems with constraints. Here we further develop this approach and present the defining system of…

We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…

We construct a commuting family of difference-evaluation operators, deforming the commuting family introduced in our earlier paper (math/9807145). We interpret them as the action of the center of quantum algebras in the space of…

Spectral properties of many finite convolution integral operators have been understood by finding differential operators that commute with them. In this paper we compile a complete list of such commuting pairs, extending previous work to…

Derivatives and integration operators are well-studied examples of linear operators that commute with scaling up to a fixed multiplicative factor; i.e., they are scale-invariant. Fractional order derivatives (integration operators) also…

For the Lie algebra $gl_N$ we introduce a system of differential operators called the dynamical operators. We prove that the dynamical differential operators commute with the $gl_N$ rational quantized Knizhnik-Zamolodchikov difference…

We give a natural generalization of the classification of commutative rings of ordinary differential operators, given in works of Krichever, Mumford, Mulase, and determine commutative rings of operators in a completed ring of partial…

In this paper we discuss some results related to commuting ordinary differential operators of rank greater than one.

We study the algebra of differential operators on non-compact simply connected harmonic manifolds and provide sufficient conditions for them to have a radial fundamental solution and be surjective on the space of smooth function.…

We construct of a family of fundamental solutions for elliptic partial differential operators with real constant coefficients. The elements of such a family are expressed by means of jointly real analytic functions of the coefficients of…

In this paper we study commuting families of holomorphic mappings in $\mathbb{C}^n$ which form abelian semigroups with respect to their real parameter. Linearization models for holomorphic mappings are been used in the spirit of…

In this paper we develop the generalised Schur theory offered in the recent paper by the second author in dimension one case, and apply it to obtain a new explicit parametrisation of torsion free rank one sheaves on projective irreducible…

We study the commutants of a Schr\"{o}dinger operator whose potential function possesses inverse square singularities along some hyperplanes passing through the origin. It is shown that the Weyl group symmetry of the potential function and…

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

We consider the Krall-Sheffer class of admissible, partial differential operators in the plane. We concentrate on algebraic structures, such as the role of commuting operators and symmetries. For the polynomial eigenfunctions, we give…

We introduce and fully analyze a new commutation relation $\overline{K} L_1 = L_2 K$ between finite convolution integral operator $K$ and differential operators $L_1$ and $L_{2}$, that has implications for spectral properties of $K$. This…

We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…

We provide sufficient conditions of local solvability for partial differential operators with variable Colombeau coefficients. We mainly concentrate on operators which admit a right generalized pseudodifferential parametrix and on operators…