Related papers: Anomaly of linearization and auxiliary integrals
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…
In this article, we explore the boundedness properties of pseudo-differential operators on radial sections of line bundles over the Poincar\'e upper half plane, even when dealing with symbols of limited regularity. We first prove the…
For linear operators which factor with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same…
Parametric factorizations of linear partial operators on the plane are considered for operators of orders two, three and four. The operators are assumed to have a completely factorable symbol. It is proved that ``irreducible'' parametric…
We present a generalized version of the discretization-invariant neural operator and prove that the network is a universal approximation in the operator sense. Moreover, by incorporating additional terms in the architecture, we establish a…
It is known that multiplication of linear differential operators over ground fields of characteristic zero can be reduced to a constant number of matrix products. We give a new algorithm by evaluation and interpolation which is faster than…
This article addresses linear hyperbolic partial differential equations and pseudodifferential equations with strongly singular coefficients and data, modelled as members of algebras of generalised functions. We employ the recently…
The problem of equivalency for linear differential operators of the first order is discussed.
The compact explicit expressions for formal exact operator solutions to Cauchy problem for sufficiently general systems of nonlinear differential equations (ODEs and PDEs) in the form of chronological operator exponents are given. The…
Complex-linearization of a class of systems of second order ordinary differential equations (ODEs) has already been studied with complex symmetry analysis. Linearization of this class has been achieved earlier by complex method, however,…
In this note we study the application of generalized fractional operators to a particular class of nonstandard Lagrangians. These are typical of dissipative systems and the corresponding Euler-Lagrange and Hamilton equations are analyzed.…
We describe the orbit structure for the action of the centralizer group of a linear operator on a finite-dimensional complex vector space. The main application is to the classification of solutions to a system of first-order ODEs with…
A previous article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs. They have infinite-dimensional Lie point symmetry groups…
We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are…
We study mapping properties of two-dimensional linear integral operators in some weighted spaces with special kernels. The considered spaces are certain variant of Sobolev--Slobodetskii spaces and their generalizations related to Banach…
We consider the possibility of adding a Grassmann-odd function \nu to the odd Laplacian. Requiring the total \Delta operator to be nilpotent leads to a differential condition for \nu, which is integrable. It turns out that the odd function…
It is sometimes desirable to produce for a nonlinear system of ODEs a new representation of simpler structural form, but it is well known that this goal may imply an increase in the dimension of the system. This is what happens if in this…
We consider the problem of discretizing evolution operators of linear delay equations with the aim of approximating their spectra, which is useful in investigating the stability properties of (nonlinear) equations via the principle of…
A method of the formal diagonalization of the discrete linear operator with a parameter is studied. In the case when the operator provides a Lax operator for a nonlinear quad system the formal diagonalization method allows one to describe…
The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting examples and consequences are given. As an illustrative…