相关论文: Weakly nonlocal Poisson brackets, Schouten bracket…

We study Dirichlet forms defined by nonintegrable L\'evy kernels whose singularity at the origin can be weaker than that of any fractional Laplacian. We show some properties of the associated Sobolev type spaces in a bounded domain, such as…

We inquire into the relation between the curl operators, the Poisson coboundary operators and contravariant derivatives on Poisson manifolds to study the theory of differential operators in Poisson geometry. Given an oriented Poisson…

In this paper, we define in an intrinsic way operators on a compact Lie group by means of symbols using the representations of the group. The main purpose is to show that these operators form a symbolic pseudo-differential calculus which…

In this paper a double quasi Poisson bracket in the sense of Van den Bergh is constructed on the space of noncommutative weights of arcs of a directed graph embedded in a disk or cylinder $\Sigma$, which gives rise to the quasi Poisson…

We call a bounded linear operator acting between Banach spaces weakly compactly generated ($\mathsf{WCG}$ for short) if its range is contained in a weakly compactly generated subspace of its codomain. This notion simultaneously generalises…

Reversible evolution of macroscopic and mesoscopic systems can be conveniently constructed from two ingredients: an energy functional and a Poisson bracket. The goal of this paper is to elucidate how the Poisson brackets can be constructed…

We consider the questions connected with the Hamiltonian properties of the Whitham equations in case of several spatial dimensions. An essential point of our approach here is a connection of the Hamiltonian structure of the Whitham system…

In this article we present the first results on domain decomposition methods for nonlocal operators. We present a nonlocal variational formulation for these operators and establish the well-posedness of associated boundary value problems,…

Continuous formal deformations of the Poisson superbracket defined on compactly supported smooth functions on n-dimensional space taking values in a Grassmann algebra with m generating elements are described up to an equivalence…

This work contains a brief and elementary exposition of the foundations of Poisson and symplectic geometries, with an emphasis on applications for Hamiltonian systems with second-class constraints. In particular, we clarify the geometric…

We develop a model in which interactions between nodes of a dynamic network are counted by non homogeneous Poisson processes. In a block modelling perspective, nodes belong to hidden clusters (whose number is unknown) and the intensity…

In this paper the well-known Dubrovin-Novikov problem posed as long ago as 1984 in connection with the Hamiltonian theory of systems of hydrodynamic type, namely, the classification problem for multidimensional Poisson brackets of…

According to the Weinstein splitting theorem, any Poisson manifold is locally, near any given point, a product of a symplectic manifold with another Poisson manifold whose Poisson structure vanishes at the point. Similar splitting results…

Toric differential inclusions play a pivotal role in providing a rigorous interpretation of the connection between weak reversibility and the persistence of mass-action systems and polynomial dynamical systems. We introduce the notion of…

Multivariate Poisson random variables subject to linear integer constraints arise in several application areas, such as queuing and biomolecular networks. This note shows how to compute conditional statistics in this context, by employing…

In potential theory, use of barriers is one of the most important techniques. We construct strong barriers for weighted quasilinear elliptic operators. There are two applications: (i) solvability of Poisson-type equations with boundary…

It is shown that the operator space generated by peripheral eigenvectors of a unital completely positive map on a von Neumann algebra has a $C^*$-algebra structure. This extends the notion of non-commutative Poisson boundary by including…

The widely accepted approach to the foundation of quantum mechanics is that the Poisson bracket, governing the non-commutative algebra of operators, is taken as a postulate with no underlying physics. In this manuscript, it is shown that…

We give a definition of coisotropic morphisms of shifted Poisson (i.e. $P_n$) algebras which is a derived version of the classical notion of coisotropic submanifolds. Using this we prove that an intersection of coisotropic morphisms of…

We consider square-integrable functionals of Poisson point processes for which the variance upper bound provided by the classical Poincar\'{e} inequality is suboptimal, a phenomenon known as superconcentration. In this paper, we establish a…