Using representation-theoretic methods, we determine the spectrum of the 2 × 2 system Q(x, Dx) = A(-∂x/2/2 + x2/2) + B(x∂x + 1/2), x ∈ R, with A,B ∈ Mat2(R) constant matrices such that A = tA > 0 (or < 0), B = -tB ≠ 0, and the Hermitian matrix A + iB positive (or negative) definite. We also give results that generalize (in a possible direction) the main construction.
Oscillator representations and systems of ordinary differential equations
Parmeggiani A.;
2001
Abstract
Using representation-theoretic methods, we determine the spectrum of the 2 × 2 system Q(x, Dx) = A(-∂x/2/2 + x2/2) + B(x∂x + 1/2), x ∈ R, with A,B ∈ Mat2(R) constant matrices such that A = tA > 0 (or < 0), B = -tB ≠ 0, and the Hermitian matrix A + iB positive (or negative) definite. We also give results that generalize (in a possible direction) the main construction.File in questo prodotto:
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