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

Liping Li; Xiucui Song

doi:10.1007/s11425-014-0869-1

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arXiv · 1505.03311

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

Liping Li·Xiucui Song

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Abstract

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.

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Liping Li, Xiucui Song. 2015-05-13. The $\alpha$-orthogonal complements of regular subspaces of 1-dim Brownian motion. https://doi.org/10.1007/s11425-014-0869-1

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