科研之友
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摘要
The number of self-adjoint extensions of a symmetric operator acting on a complex Hilbert space is characterized by its deficiency indices. Given a locally finite unoriented simple tree, we prove that the deficiency indices of any discrete Schrodinger operator are either null or infinite. We also prove that all deterministic discrete Schrodinger operators which act on a random tree are almost surely self-adjoint. Furthermore, we provide several criteria of essential self-adjointness. We also address some importance to the case of the adjacency matrix and conjecture that, given a locally finite unoriented simple graph, its deficiency indices are either null or infinite. Besides that, we consider some generalizations of trees and weighted graphs.
- 出版日期2011-6
