Eigenvalue Multiplicities for Second Order Elliptic Operators on Networks Joachim
نویسندگان
چکیده
We present some general bounds for the algebraic and geometric multiplicity of eigenvalues of second order elliptic operators on finite networks under continuity and weighted Kirchhoff flow conditions at the vertices. In particular the algebraic multiplicity of an eigenvalue is shown to be strictly bounded from above by the number of vertices if there are no eigenfunctions vanishing in all nodes, and to be bounded from above by the number of edges if there are such eigenfunctions. Mathematics subject classification (2010): 34B45, 34L20, 05C50, 35J25, 34L10.
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تاریخ انتشار 2013