Oscillator representations and systems of ordinary differential equations.
Using representation-theoretic methods, we determine the spectrum of the 2 x 2 system. Q(x, D(x)) = A- partial differential(2)(x)2 + x(2)2 + Bx partial differential(x) + 1/2, x in, with A, B in Mat(2)(R) constant matrices such that A = (t)A > 0 (or <0), B = -(t)B not equal 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
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Department of Mathematics, University of Bologna, Piazza di Porta S. Donato 5, 40127 Bologna, Italy.
Wakayama
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