Trees with Cantor Eigenvalue Distribution | Zendy

He Li | Zendy; Liu Xiangwei | Zendy; Strang Gilbert | Zendy

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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 .

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