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Trees with Cantor Eigenvalue Distribution
Author(s) -
He Li,
Liu Xiangwei,
Strang Gilbert
Publication year - 2003
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00233
Subject(s) - eigenvalues and eigenvectors , mathematics , adjacency matrix , degree (music) , piecewise , combinatorics , constant (computer programming) , tree (set theory) , mathematical analysis , pure mathematics , graph , physics , quantum mechanics , computer science , acoustics , programming language
We study a family of trees with degree k at all interior nodes and degree 1 at boundary nodes. The eigenvalues of the adjacency matrix have high multiplicities. As the trees grow, the graphs of those eigenvalues approach a piecewise‐constant “Cantor function.” For each value of , we will find the fraction of the eigenvalues that are given by .