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Bounds on the Multiplicity of Eigenvalues for Fixed Membranes

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Abstract.

For a membrane in the plane the multiplicity of the k-th eigenvalue is known to be not greater than 2k— 1. Here we prove that it is actually not greater than 2k— 3, for \( k \ge 3 \).

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Authors and Affiliations

  1. Inst. für Theor. Chemie, Universität Wien, Währinger Straße 17, A-1090 Wien, Austria, and: Erwin Schrödinger, Inst. für Math. Physik, Boltzmanngasse 9, A-1090 Wien, Austria, e-mail: thoffman@esi.ac.at, , , , , , AT

    T. Hoffmann-Ostenhof

  2. Inst. für Math., Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria, and: Erwin Schrödinger, Inst. für Math. Physik, Boltzmanngasse 9, A-1090 Wien, Austria, e-mail: peter.michor@esi.ac.at, , , , , , AT

    P. W. Michor

  3. Dept. of Mathematics, MIT, Cambridge, MA 02139, USA, , , , , , US

    N. Nadirashvili

Authors
  1. T. Hoffmann-Ostenhof
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  2. P. W. Michor
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  3. N. Nadirashvili
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Submitted: March 1998, revised: May 1999.

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Hoffmann-Ostenhof, T., Michor, P. & Nadirashvili, N. Bounds on the Multiplicity of Eigenvalues for Fixed Membranes . GAFA, Geom. funct. anal. 9, 1169–1188 (1999). https://doi.org/10.1007/s000390050111

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  • DOI: https://doi.org/10.1007/s000390050111

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