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URN etd-0723108-112710
Author Chien-Ru Lin
Author's Email Address No Public.
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Department Applied Mathematics
Year 2007
Semester 2
Degree Master
Type of Document
Language English
Title Ambarzumyan problem on trees
Date of Defense 2008-05-30
Page Count 58
Keyword
  • Ambarzumyan problem
  • Sturm-Liouville operator
  • Dirichlet boundary problem
  • Neumann boundary problem
  • Tree
  • Abstract We study the Ambarzumyan problem for Sturm-Liouville operator defined on graph. The classical Ambarzumyan Theorem states that if the Neumann eigenvalues of the Sturm-Liouville operator defined on
    the interval [0,π] are exactly {n^2: n ∈ N ⋃ {0} }, then the potential q=0. In 2005, Pivovarchik proved two similar theorems with uniform lengths a for the Sturm-Liouville operator defined on a 3-star graphs. Then Wu considered the Ambarzumyan problem for graphs
    of nonuniform length in his thesis. In this thesis, we shall study the Ambarzumyan problem on more complicated trees, namely, 4-star graphs and caterpillar graphs with edges of different lengths. We
    manage to solve the Ambarzumyan problem for both Neumann eigenvalues and Dirichlet eigenvalues. In particular, the whole spectrum can be partitioned into several parts. Each part forms the solution to one
    Ambarzumyan problem. For example, for a 4-star graphs with edge lengths a, a, 2a, 2a form the solution to 3 different Ambarzumyan problems for the Neumann eigenvalues.
    Advisory Committee
  • Xuding Zhu - chair
  • Wei-Cheng Lian - co-chair
  • Chun-Kong Law - advisor
  • Files
  • etd-0723108-112710.pdf
  • indicate accessible in a year
    Date of Submission 2008-07-23

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