Related papers: Linear difference operators with sequence coeffici…
For a linear difference equation with the coefficients being computable sequences, we establish algorithmic undecidability of the problem of determining the dimension of the solution space including the case when some additional prior…
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…
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…
Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance…
A complete classification of linear differential operators possessing finite-dimensional invariant subspace with a basis of monomials is presented.
Different index concepts for linear differential-algebraic equations are defined in the general Banach space setting, and compared. For regular finite-dimensional linear differential-algebraic equations, all these indices exist and are…
We give criteria for finite dimensionality or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative invariants of the group. In the finite dimensional scenario…
In this paper we derive structure theorems that characterize the spaces of linear and non-linear differential operators that preserve finite dimensional subspaces generated by polynomials in one or several variables. By means of the useful…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
We give new examples of linear differential operators of order $k=2m+1$ (any given odd integer) that are invariant under the isometries of $\mathbb R^n$ and satisfy so-called $L^1$-duality estimates and div/curl inequalities.
A vector space S of linear operators between finite-dimensional vector spaces U and V is called locally linearly dependent (in abbreviate form: LLD) when every vector x in U is annihilated by a non-zero operator in S. By a duality argument,…
This paper extends the discriminant associated to second order linear constant coefficient differential equations to general second order linear differential equations. The main result of this paper is that the discriminant of a second…
In this paper, we generalize the fractional order difference operator using $l$- Pochhammer symbol and define $l$- fractional difference operator. The $l$- fractional difference operator is further used to introduce a class of difference…
We consider difference operators in $L^2$ on $\R$ of the form $$ L f(s)=p(s)f(s+i)+q(s) f(s)+r(s) f(s-i) ,$$ where $i$ is the imaginary unit. The domain of definiteness are functions holomorphic in a strip with some conditions of decreasing…
In this paper we consider a reduction of a non-homogeneous linear system of first order operator equations to a totally reduced system. Obtained results are applied to Cauchy problem for linear differential systems with constant…
In this paper, the linear differential expression of order $n \ge 2$ with distribution coefficients of various singularity orders is considered. We obtain the associated matrix for the regularization of this expression. Furthermore, we…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
This paper is the second part of our series of works to establish $L^2$ estimates and existence theorems for the $\overline{\partial}$ operators in infinite dimensions. In this part, we consider the most difficult case, i.e., the underlying…
We study infinite order differential operators acting in the spaces of exponential type entire functions. We derive conditions under which such operators preserve the set of Laguerre entire functions which consists of the polynomials…
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…