Related papers: On Selfadjoint Subspace of One-Speed Boltzmann Ope…
Problems associated with the Boltzmann collisional operator are unveiled and discussed. By careful investigation it is shown that collective effects of molecular collisions in the six-dimensional position and velocity space are more…
The construction of discrete velocity models or numerical methods for the Boltzmann equation, may lead to the necessity of computing the collision operator as a sum over lattice points. The collision operator involves an integral over a…
The Boltzmann equation without an angular cutoff is considered when the initial data is a small perturbation of a global Maxwellian with an algebraic decay in the velocity variable. A well-posedness theory in the perturbative framework is…
The linearized Boltzmann collision operator is fundamental in many studies of the Boltzmann equation and its main properties are of substantial importance. The decomposition into a sum of a positive multiplication operator, the collision…
The linearized Boltzmann collision operator has a central role in many important applications of the Boltzmann equation. Recently some important classical properties of the linearized collision operator for monatomic single species were…
Based on the recent construction of a self-adjoint momentum operator for a particle confined in a one-dimensional interval, we extend the construction to arbitrarily shaped regions in any number of dimensions. Different components of the…
We study spectral properties of one-dimensional singular perturbations of an unbounded selfadjoint operator and give criteria for the possibility to remove the whole spectrum by a perturbation of this type. A counterpart of our results for…
The linearized collision operator of the Boltzmann equation for single species can be written as a sum of a positive multiplication operator, the collision frequency, and a compact integral operator. This classical result has more recently,…
In this paper we explore a certain class of non-selfadjoint operators acting in a complex separable Hilbert space. We consider a perturbation of a non-selfadjoint operator by an operator that is also non-selfadjoint. Our consideration is…
The linearized collision operator of the Boltzmann equation can in a natural way be written as a sum of a positive multiplication operator, the collision frequency, and an integral operator. Compactness of the integral operator for…
We define functions of noncommuting self-adjoint operators with the help of double operator integrals. We are studying the problem to find conditions on a function $f$ on ${\Bbb R}^2$, for which the map $(A,B)\mapsto f(A,B)$ is Lipschitz in…
A linear Boltzmann equation with nonautonomous collision operator is rigorously derived in the Boltzmann-Grad limit for the deterministic dynamics of a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions with…
In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Newmann for symmetric operators in order to determine whether the…
This text is a survey of recent results obtained by the author and collaborators on different problems for non-self-adjoint operators. The topics are: Kramers-Fokker-Planck type operators, spectral asymptotics in two dimensions and Weyl…
This work is devoted to the analysis of the linear Boltzmann equation in a bounded domain, in the presence of a force deriving from a potential. The collision operator is allowed to be degenerate in the following two senses: (1) the…
We present a convergence theory for Optimized Schwarz Methods that rely on a non-local exchange operator and covers the case of coercive possibly non-self-adjoint impedance operators. This analysis also naturally deals with the presence of…
We give a spectral description of the semi-classical Schrodinger operator with a piecewise linear, complex valued potential. Moreover, using these results, we show how an arbitrarily small bounded perturbation of a non-self-adjoint operator…
We prove a new criterion that guarantees self-adjointness of Toeplitz operator with unbounded operator-valued symbols. Our criterion applies, in particular, to symbols with Lipschitz continuous derivatives, which is the natural class of…
In this paper, we investigate a compactness property of the linearized Boltzmann operator in the context of a polyatomic gas whose molecules undergo resonant collisions. The peculiar structure of resonant collision rules allows to tensorize…
We consider physical interpretations of non-trivial boundary conditions of self-adjoint extensions for one-dimensional Schr\"odinger operator of free spinless particle. Despite its model and rather abstract character this question is worth…