Oscillator representations and systems of ordinary differential equations

Authors
Parmeggiani, A Wakayama, M
Citation
A. Parmeggiani et M. Wakayama, Oscillator representations and systems of ordinary differential equations, P NAS US, 98(1), 2001, pp. 26-30
Citations number
12
Categorie Soggetti
Multidisciplinary
Journal title
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
ISSN journal
00278424 → ACNP
Volume
98
Issue
1
Year of publication
2001
Pages
26 - 30
Database
ISI
SICI code
0027-8424(20010102)98:1<26:ORASOO>2.0.ZU;2-X
Abstract
Using representation-theoretic methods. we determine the spectrum of the 2 x 2 system Q(x, D-x) = A(-partial derivative (2)(x)/2 + x(2)/2) + B(x partial derivati ve (x) + 1/2), x is an element of R, with A, B is an element of Mat(2)(R) constant matrices such that A = (t)A > 0 (or <0), B = -B-t <not equal> 0, and the Hermitian matrix A + iB positiv e (or negative) definite. We also give results that generalize (in a possib le direction) the main construction.