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Spectral properties of compact multiparameter operators

  • Paul Binding (a1), Patrick J. Browne (a1) and Lawrence Turyn (a2)

Synopsis

Let

be, for each λ∈ℝk, a compact symmetric operator on a complex Hilbert space. Let the“fundamental” eigenset Z be denned by the relation λ∈Z if and only if W(λ) has maximal eigenvalue one. Conditions are given for Z to be the boundary of an open convex set P. A detailed investigation is given of the structure of P, including its recession cone and its representations as intersections of half-spaces.

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References

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7Hadeler, K. P.. Mehrparametrige und nichtlineare Eigenwertaufgaben. Arch. Rational Mech. Anal. 27 (1967), 306328.
8Pell, A. J.. Linear equations with two parameters. Trans. Amer. Math. Soc. 23(1922), 198211.
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10Richardson, R. G. D.. Über die notwendig und hinreichenden Bedingungen für das Bestehen eines Kleinschen Oszillationstheorems Math. Ann. 73 (1912/1913), 289304.
11Rockafellar, R. T.. Convex Analysis (Princeton University Press, 1970).
12Turyn, L.. Sturm-Liouville problems with several parameters. J. Differential Equations 38 (1980), 239259.

Spectral properties of compact multiparameter operators

  • Paul Binding (a1), Patrick J. Browne (a1) and Lawrence Turyn (a2)

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