A structured inverse spectrum problem for infinite graphs

作者：Monfared Keivan Hassani; Khanmohammadi Ehssan^*

来源：Linear Algebra and Its Applications, 2018, 539: 28-43.

DOI：10.1016/j.laa.2017.10.025

• Inverse spectrum problem
• Jacobian method
• Infinite graph
• Isospectral
• Essential spectrum
• Approximate unitary equivalence

In this paper it is shown that for a given infinite graph G on countably many vertices, and a compact, infinite set A of real numbers there is a real symmetric matrix A whose graph is G and its spectrum is A. Moreover, the set of limit points of A equals the essential spectrum of A, and the isolated points of A are eigenvalues of A with multiplicity one. It is also shown that any two such matrices constructed by our method are approximately unitarily equivalent.

• 出版日期2018-2-15