Abstract
We consider linear operators lying in the orthogonal group of a quadratic form and study those spectral properties of such operators that can be expressed in terms of the signature of this form. We show that in the typical case these transformations are symplectic. Some of the results can be extended to the general case when the operator admits a homogeneous form of degree ≥3.
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Original Russian Text © V.V. Kozlov, 2010, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Vol. 268, pp. 155–167.
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Kozlov, V.V. Spectral properties of operators with polynomial invariants in real finite-dimensional spaces. Proc. Steklov Inst. Math. 268, 148–160 (2010). https://doi.org/10.1134/S0081543810010128
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DOI: https://doi.org/10.1134/S0081543810010128