Related papers: Separable Quadratic Stochastic Operators
Notion of an open system of second order is introduced. Characteristic function for such an open system is obtained. Model representations of a quadratic non-self-adjoint operator pencil are found.
Finiteness of the point spectrum of linear operators acting in a Banach space is investigated from point of view of perturbation theory. In the first part of the paper we present an abstract result based on analytical continuation of the…
A continuous linear operator L defined on the space of entire functions H(C) is said to be an extended $lambda$-eigenoperator of the differentiation operator D provided DL = $lambda$LD. Here we fully characterize when an extended…
In this paper, we introduce and study a new class of bounded linear operators on complex Hilbert spaces, which we call 2-C-normal operators. This class is inspired by and closely related to the notion of 2-normal operators, with additional…
This note is concerned with an important for modelling question of existence of solutions of stochastic partial differential equations as proper stochastic processes, rather than processes in the generalized sense. We consider a first order…
We propose that classical random matrix models are properly viewed as finite difference schemes for stochastic differential operators. Three particular stochastic operators commonly arise, each associated with a familiar class of local…
In a previous paper I showed how the ideal SLAC derivative and second-derivative operators for an infinite lattice can be obtained in simple closed form in position space, and implemented very efficiently in a stochastic fashion for…
Biquaternionic Vekua-type equations arising from the factorization of linear second order elliptic operators are studied. Some concepts from classical pseudoanalytic function theory are generalized onto the considered spatial case. The…
This article proposed a new approach to the determination of the spectrum for nonlinear continuous operators in the Banach spaces and using it investigated the spectrum of some classes of operators. Here shows that in nonlinear operators…
The entanglement in operator space is a well established measure for the complexity of the quantum many-body dynamics. In particular, that of local operators has recently been proposed as dynamical chaos indicator, i.e. as a quantity able…
We characterize disjoint hypercyclic sequences of wedge operators. Also, we give some sufficient conditions for a sequence of the dual wedge operators to be disjoint topologically transitive. Finally, we give some concrete examples and…
The first step in the counting operator analysis of the spectrum of any model Hamiltonian H is the choice of a Hermitean operator M in such a way that the third commutator with H is proportional to the first commutator. Next one calculates…
Reduction operators, i.e. the operators of nonclassical (or conditional) symmetry of a class of variable coefficient nonlinear wave equations with power nonlinearities is investigated within the framework of singular reduction operator. A…
We consider second-order functional differential operators with a constant delay. Properties of their spectral characteristics are obtained and a nonlinear inverse problem is studied, which consists in recovering the operators from their…
We obtain sharp uniform bounds on the low lying eigenfunctions for a class of semiclassical pseudodifferential operators with double characteristics and complex valued symbols, under the assumption that the quadratic approximations along…
In this paper, we initiate the study of a new interrelation between linear ordinary differential operators and complex dynamics which we discuss in details in the simplest case of operators of order $1$. Namely, assuming that such an…
Many systems in physics, chemistry and biology exhibit oscillations with a pronounced random component. Such stochastic oscillations can emerge via different mechanisms, for example linear dynamics of a stable focus with fluctuations,…
This paper investigates a conditional mean-field type linear quadratic (LQ) optimal control problem with partial observation and regime switching, where the conditional expectations of the state and control given the history of Markov chain…
In this article, we show that multilinear fractional type operators are bounded from product Hardy spaces with variable exponents into Lebesgue spaces with variable exponents via the atomic decomposition theory. We also study continuity…
We introduce a notion of $\ell$-Volterra quadratic stochastic operator defined on $(m-1)$-dimensional simplex, where $\ell\in\{0,1,...,m\}$. The $\ell$-Volterra operator is a Volterra operator iff $\ell=m$. We study structure of the set of…