Related papers: Rational recursion operators for integrable differ…
We solve the problem of describing all nonlocal Hamiltonian operators of hydrodynamic type with flat metrics. This problem is also equivalent to the description of all flat submanifolds with flat normal bundle in a pseudo-Euclidean space.…
Reduction operators (called also nonclassical or $Q$-conditional symmetries) of variable coefficient semilinear reaction-diffusion equations with exponential source $f(x)u_t=(g(x)u_x)_x+h(x)e^{mu}$ are investigated using the algorithm…
We prove that a local Hamiltonian operator of hydrodynamic type K_1 is compatible with a nondegenerate local Hamiltonian operator of hydrodynamic type K_2 if and only if the operator K_1 is locally the Lie derivative of the operator K_2…
We establish a discrete operator--theoretic framework for the analysis of implicit Euler and Lie--Trotter splitting schemes for delay differential equations (DDEs). Both schemes are formulated in terms of discrete resolvent operators acting…
In this note we describe how the Neumann homogenization of fully nonlinear elliptic equations can be recast as the study of nonlocal (integro-differential) equations involving elliptic integro-differential operators on the boundary. This is…
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…
Inverse problems are important mathematical problems that seek to recover model parameters from noisy data. Since inverse problems are often ill-posed, they require regularization or incorporation of prior information about the underlying…
The purpose of this paper is to introduce an algebraic cohomology theory of left pre-Jacobi-Jordan algebras. We use the cohomological approach to study linear deformations of these algebras. We also introduce the notion of Nijenhuis…
A well known tool in conventional (von Neumann) quantum mechanics is the self-adjoint extension technique for symmetric operators. It is used, e.g., for the construction of Dirac-Hermitian Hamiltonians with point-interaction potentials.…
We define and derive basic properties of the notion of Rota-Baxter operator on anti-flexible algebra. Starting from a Rota-Baxter operator on an anti-flexible algebra, we construct pre-anti-flexible algebra structure and associated…
For a class of non-selfadjoint $h$--pseudodifferential operators with double characteristics, we give a precise description of the spectrum and establish accurate semiclassical resolvent estimates in a neighborhood of the origin.…
We explicitly construct a finite number of discrete components in the restriction of complementary series representations of rank one semisimple groups $G$ to rank one subgroups $G_1$. For this we use the realizations of complementary…
In this note we set up the elliptic and the parabolic Dirichlet problem for linear nonlocal operators. As opposed to the classical case of second order differential operators, here the "boundary data" are prescribed on the complement of a…
Operator splitting methods allow to split the operator describing a complex dynamical system into a sequence of simpler subsystems and treat each part independently. In the modeling of dynamical problems, systems of (possibly coupled)…
The fundamental tool in the classification of orthogonal coordinate systems in which the Hamilton-Jacobi and other prominent equations can be solved by a separation of variables are second order Killing tensors which satisfy the Nijenhuis…
Let $Q$ be a differential operator of order $\leq 1$ on a complex metric vector bundle $\mathscr{E}\to \mathscr{M}$ with metric connection $\nabla$ over a possibly noncompact Riemannian manifold $\mathscr{M}$. Under very mild regularity…
On a suitable class of non-compact manifolds, we study (pseudo)differential operators which feature an asymptotic translation-invariance along one axis and an asymptotic dilation-invariance, or asymptotic homogeneity with respect to…
We extend the Ruzhansky-Turunen theory of pseudo differential operators on compact Lie groups into a tool that can be used to investigate group-valued Markov processes in the spirit of the work in Euclidean spaces of N.Jacob and…
First, we study the subskewfield of rational pseudodifferential operators over a differential field K generated in the skewfield of pseudodifferential operators over K by the subalgebra of all differential operators. Second, we show that…
In this paper, we first study infinitesimal deformations of a Lie conformal algebra and a Lie conformal algebra with a module (called an $\mathsf{LCMod}$ pair), which lead to the notions of Nijenhuis operator on the Lie conformal algebra…