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Spectral properties of operators with polynomial invariants in real finite-dimensional spaces. (English. Russian original) Zbl 1209.47005
Proc. Steklov Inst. Math. 268, 148-160 (2010); translation from Trudy Mat. Inst. Steklova 268, 155-167 (2010).
The author considers linear operators lying in the orthogonal group of a quadratic form and studies those spectral properties of such operators that can be expressed in terms of the signature of this form. He shows 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 $$\geq 3$$.

##### MSC:
 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 47A10 Spectrum, resolvent 34C14 Symmetries, invariants of ordinary differential equations 47A75 Eigenvalue problems for linear operators
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