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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/41516

    Title: A vectorial inverse nodal problem
    Authors: Cheng, Yan-hsiou;Shieh, Chung-tsun;謝忠村;Law, C. K.
    Contributors: 淡江大學數學學系
    Date: 2005-05
    Issue Date: 2010-01-28 07:44:02 (UTC+8)
    Publisher: Providence: American Mathematical Society (AMS)
    Abstract: Consider the vectorial Sturm-Liouville problem:
    −y''(x) + P(x)y(x) = λIdy(x)
    Ay(0) + Idy(0) = 0
    By(1) + Idy(1) = 0
    where P(x)=[pij(x)]d i,j=1 is a continuous symmetric matrix-valued function
    defined on [0, 1], and A and B are d×d real symmetric matrices. An eigenfunction
    y(x) of the above problem is said to be of type (CZ) if any isolated zero
    of its component is a nodal point of y(x). We show that when d = 2, there
    are infinitely many eigenfunctions of type (CZ) if and only if (P(x), A, B) are
    simultaneously diagonalizable. This indicates that (P(x), A, B) can be reconstructed when all except a finite number of eigenfunctions are of type (CZ).
    The results supplement a theorem proved by Shen-Shieh (the second author)
    for Dirichlet boundary conditions. The proof depends on an eigenvalue estimate,
    which seems to be of independent interest.
    Relation: Proceedings of the American Mathematical Society 133(5), pp.1475-1484
    DOI: 10.1090/S0002-9939-04-07679-8
    Appears in Collections:[Graduate Institute & Department of Mathematics] Journal Article

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