RT Journal Article
T1 A Perturbation of the Dunkl Harmonic Oscillator on the Line
A1 Álvarez López, Jesús Antonio
A1 Calaza Cabanas, Manuel
A1 Franco, Carlos
K1 Dunkl harmonic oscillator
K1 Perturbation theory
AB Let Jσ be the Dunkl harmonic oscillator on R (σ>−1/2. For 0<u<1 and ξ>0, it is proved that, if σ>u−1/2, then the operator U=Jσ+ξ|x|−2u, with appropriate domain, is essentially self-adjoint in L2(R,|x|2σdx), the Schwartz space S is a core of U¯¯¯¯1/2, and U¯¯¯¯ has a discrete spectrum, which is estimated in terms of the spectrum of Jσ¯¯¯¯¯. A generalization Jσ,τ of Jσ is also considered by taking different parameters σ and τ on even and odd functions. Then extensions of the above result are proved for Jσ,τ, where the perturbation has an additional term involving, either the factor x−1 on odd functions, or the factor x on even functions. Versions of these results on R+ are derived
PB National Academy of Science of Ukraine
YR 2015
FD 2015
LK http://hdl.handle.net/10347/21868
UL http://hdl.handle.net/10347/21868
LA eng
NO Álvarez López, J. A., Calaza, M., and Franco, C. (2015). A perturbation of the Dunkl harmonic oscillator on the line. Symmetry, Integrability and Geometry: Methods and Applications.
NO The first author was partially supported by MICINN, Grants MTM2011-25656 and MTM2014-56950-P, and by Xunta de Galicia, Grant Consolidación e estructuración 2015 GPC GI-1574. The third author has received financial support from the Xunta de Galicia and the European Union (European Social Fund - ESF)
DS Minerva
RD 4 may 2026