A Perturbation of the Dunkl Harmonic Oscillator on the Line

被引:2
|
作者
Alvarez Lopez, Jesus A. [1 ]
Calaza, Manuel [2 ,3 ]
Franco, Carlos
机构
[1] Univ Santiago de Compostela, Fac Matemat, Dept Xeometria & Topoloxia, Santiago De Compostela 15782, Spain
[2] Hosp Clin Univ Santiago, Lab Invest 2, Santiago De Compostela, Spain
[3] Hosp Clin Univ Santiago, Rheumatol Unit, Santiago De Compostela, Spain
关键词
Dunkl harmonic oscillator; perturbation theory;
D O I
10.3842/SIGMA.2015.059
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let J(sigma) be the Dunkl harmonic oscillator on R (sigma > -1/2). For 0 < u < 1 and xi > 0, it is proved that, if sigma > u - 1/2, then the operator U = J(sigma) + xi vertical bar x vertical bar(-2u), with appropriate domain, is essentially self-adjoint in L-2 (R,vertical bar x vertical bar(2 sigma)dx), the Schwartz space S is a core of (U) over bar (1/2) and (U) over bar has a discrete spectrum, which is estimated in terms of the spectrum of (J) over bar (sigma). A generalization J(sigma),(tau) of J(sigma) is also considered by taking different parameters sigma and tau on even and odd functions. Then extensions of the above result are proved for J(sigma,tau), 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.
引用
收藏
页数:33
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