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.

Parmeggiani A., Wakayama M. (2001). Oscillator representations and systems of ordinary differential equations. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 98(1), 26-30 [10.1073/pnas.98.1.26].

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.
2001
Parmeggiani A., Wakayama M. (2001). Oscillator representations and systems of ordinary differential equations. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 98(1), 26-30 [10.1073/pnas.98.1.26].
Parmeggiani A.; Wakayama M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/893775
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