Oscillator representations and systems of ordinary differential equations.

@article{Parmeggiani2001OscillatorRA,
  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},
  year={2001},
  volume={98 1},
  pages={26-30}
}
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. 
Related Discussions
This paper has been referenced on Twitter 1 time. VIEW TWEETS

From This Paper

Topics from this paper.

Citations

Publications citing this paper.
Showing 1-10 of 11 extracted citations

References

Publications referenced by this paper.
Showing 1-7 of 7 references

A Necessary and Sufficient Condition for Melin’s Inequality for a Class of Systems, preprint

R. Brummelhuis, J. Nourrigat
2000

Non-Commutative Harmonic Oscillators II, preprint

A. Parmeggiani, M. Wakayama
2000

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

A. Parmeggiani, M. Wakayama
2000

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

H. Ochiai
1999

Non-Commutative Harmonic Oscillators I, preprint

A. Parmeggiani, M. Wakayama
1998
View 1 Excerpt

On Melin’s Inequality for Systems, preprint

R. Brummelhuis
1997

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

R. Howe, E. C. Tan
1992

Similar Papers

Loading similar papers…