Oscillator representations and systems of ordinary differential equations

Parmeggiani, Alberto; Wakayama, Masato

Oscillator representations and systems of ordinary differential equations

Authors

Parmeggiani, Alberto

Wakayama, Masato

Publisher

National Academy of Sciences

Description

Using representation-theoretic methods, we determine the spectrum of the 2 × 2 system [Formula: see text] with A, B ∈ Mat(2)(ℝ) constant matrices such that A = (t)A > 0 (or <0), B = −(t)B ≠ 0, and the Hermitian matrix A + iB positive (or negative) definite. We also give results that generalize (in a possible direction) the main construction.