Related papers: Extension of Hereditary Symmetry Operators
An analysis of extension of Hamiltonian operators from lower order to higher order of matrix paves a way for constructing Hamiltonian pairs which may result in hereditary operators. Based on a specific choice of Hamiltonian operators of…
We introduce a notion of ``hereditarily antisymmetric'' operator algebras and prove a structure theorem for them in finite dimensions. We also characterize those operator algebras in finite dimensions which can be made upper triangular and…
A Hamiltonian pair with arbitrary constants is proposed and thus a sort of hereditary operators is resulted. All the corresponding systems of evolution equations possess local bi-Hamiltonian formulation and a special choice of the systems…
Using the methods of the theory of formal symmetries, we obtain new easily verifiable sufficient conditions for a recursion operator to produce a hierarchy of local generalized symmetries. An important advantage of our approach is that…
The recursion operators and symmetries of non-autonomous, (1+1)-dimensional integrable evolution equations are considered. It has been previously observed that the symmetries of the integrable evolution equations obtained through their…
A mechanism deriving new well-posed evolutionary equations from given ones is inspected. It turns out that there is one particular spatial operator from which many of the standard evolutionary problems of mathematical physics can be…
In this paper we obtain several extension properties for monotone and sublinear operators. The results obtained generalize those known for positive and linear operators.
We study a class of evolutionary partial differential systems with two components related to second order (in time) non-evolutionary equations of odd order in spatial variable. We develop the formal diagonalisation method in symbolic…
An automorphism defined on an evolution algebra can provide both a finite number and an infinite number of evolution operators on it. This question is dealt with in the paper, as well as others more related to the evolution operators of…
This article is devoted to applications of projection operators to simulate phenomenological properties of the molecular-genetic code system. Oblique projection operators are under consideration, which are connected with matrix…
The problem of classification into symmetry integrable classes is solved for a family of second order nonlinear evolution equations labeled by arbitrary functions. Four nonequivalent symmetry integrable classes are thus obtained and the…
Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, $C$-selfadjoint…
We derive the general conditions for fully-nonlinear symmetry-integrable second-order evolution equations and their first-order recursion operators. We then apply the established Propositions to find links between a class of fully-nonlinear…
We introduce and study the notion of hereditary frequent hypercyclicity, which is a reinforcement of the well known concept of frequent hypercyclicity. This notion is useful for the study of the dynamical properties of direct sums of…
We consider the recursion operators with nonlocal terms of special form for evolution systems in (1+1) dimensions, and extend them to well-defined operators on the space of nonlocal symmetries associated with the so-called universal Abelian…
A set of Hamiltonians that are not self-adjoint but have the spectrum of the harmonic oscillator is studied. The eigenvectors of these operators and those of their Hermitian conjugates form a bi-orthogonal system that provides a…
We study generalized solutions of an evolutionary equation related to some densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and suggest…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
In this note unbounded hyperexpansive weighted composition operators are investigated. AS a consequence unbounded hyperexpansive multiplication and composition operators are characterized.
We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…