Genericity of simple eigenvalues for elliptic PDE’s

Albert, J. H.

doi:10.1090/S0002-9939-1975-0385934-4

Genericity of simple eigenvalues for elliptic PDE’s
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by J. H. Albert

Proc. Amer. Math. Soc. 48 (1975), 413-418

DOI: https://doi.org/10.1090/S0002-9939-1975-0385934-4

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Abstract:

The spectrum of a selfadjoint, ${C^\infty }$ linear elliptic partial differential operator on a compact manifold contains only isolated eigenvalues, each having finite multiplicity. It is sometimes the case that these multiplicities are unbounded; this is common in problems arising in applications because of the high degree of symmetry usually present. The main theorem shows that the property of having only simple eigenvalues is generic for operators obtained by varying the zeroth order part of a given operator.

References

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Generic properties of eigenfunctions