TY - JOUR
T1 - Oscillator representations and systems of ordinary differential equations
AU - Parmeggiani, Alberto
AU - Wakayama, Masato
PY - 2001/1/2
Y1 - 2001/1/2
N2 - 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.
AB - 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.
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U2 - 10.1073/pnas.98.1.26
DO - 10.1073/pnas.98.1.26
M3 - Article
C2 - 11134511
AN - SCOPUS:0035793063
SN - 0027-8424
VL - 98
SP - 26
EP - 30
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
IS - 1
ER -