Oscillator representations and systems of ordinary differential equations.

  title={Oscillator representations and systems of ordinary differential equations.},
  author={Alberto Parmeggiani and Masato Wakayama},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  volume={98 1},
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. 
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A Necessary and Sufficient Condition for Melin’s Inequality for a Class of Systems, preprint

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On Certain Systems of Differential Equations Associated with Lie-Algebra Representations and Their Perturbations

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Non-Commutative Harmonic Oscillators and Fuchsian Ordinary Differential Operators, preprint

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On Melin’s Inequality for Systems, preprint

R. Brummelhuis

Non-Albelian Harmonic Analysis. Applications of SL(2, R) (Springer, New York). 30 u www.pnas.org Parmeggiani and Wakayama

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