arXiv subjects

Xiucui Song

Publications and source records attributed to Xiucui Song.

3 recordsLinked to original sources

arXiv2015

The $\alpha$-orthogonal complements of regular subspaces of 1-dim Brownian motion

Roughly speaking, a regular subspace of a Dirichlet form is a subspace, which is also a regular Dirichlet form, on the same state space. In particular, the domain of regular subspace is a closed subspace of the Hilbert space induced by the domain and $\alpha$-inner product of original Dirichlet form. We shall investigate the orthogonal complement of regular subspace of 1-dimensional Brownian motion in this paper. Our main results indicate that this orthogonal complement has a very close connection with the $\alpha$-harmonic equation under Neumann boundary condition.

math.PR↗

arXiv2015

Regular Dirichlet subspaces and Mosco convergence

In this paper, we shall explore the Mosco convergence on regular subspaces of one-dimensional irreducible and strongly local Dirichlet forms. We find that if the characteristic sets of regular subspaces are convergent, then their associated regular subspaces are convergent in sense of Mosco. Finally, we shall show some examples to illustrate that the Mosco convergence does not preserve any global properties of Dirichlet forms.

math.PR↗

arXiv2015

Stickiness of KAM tori for higher dimensional beam equation

This paper is concerned with the stickiness of invariant tori obtained by KAM technics (so-called KAM tori) for higher dimensional beam equation. We prove that the KAM tori are sticky, i.e. the solutions starting in the $δ$-neighborhood of KAM torus still stay close to the KAM torus for a polynomial long time such as $|t|\leq δ^{-\mathcal{M}}$ with any $\mathcal{M}\geq 0$, by constructing a partial normal form of higher order, which satisfies $p$-tame property, around the KAM torus.

math.DS↗