2015/12/18 by Keivan Hassani Monfared, Monfared, Keivan Hassani, Ehssan Khanmohammadi +1
Mathematics · #05C50 #15A18 #15A29 #47A10 #FOS: Mathematics #Spectral Theory (math.SP) #math.SP #msc:05C50 #msc:15A18 #msc:15A29 #msc:47A10
paper · pdf · doi:10.48550/arxiv.1512.05834
arxiv created 2016/10/05 · arxiv updated 2016/10/06
It is shown that for a given infinite graph G on countably many vertices, and a compact, infinite set of real numbers Λ there is a real symmetric matrix A whose graph is G and its spectrum is Λ. Moreover, the set of limit points of Λ equals the essential spectrum of A, and the isolated points of Λ are eigenvalues of A with multiplicity one. It is also shown that any two such matrices constructed by our method are approximately unitarily equivalent.