Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 10 (2014), 004, 16 pages      arXiv:1301.4196      http://dx.doi.org/10.3842/SIGMA.2014.004

Embedding Theorems for the Dunkl Harmonic Oscillator on the Line

Jesús A. Álvarez López a and Manuel Calaza b
a) Departamento de Xeometría e Topoloxía, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
b) Laboratorio de Investigación 10, Servicio de Reumatología, Instituto de Investigaciółn Sanitaria, Hospital Clínico Universitario, 15706 Santiago de Compostela, Spain

Received September 09, 2013, in final form January 06, 2014; Published online January 10, 2014

Abstract
Embedding results of Sobolev type are proved for the Dunkl harmonic oscillator on the line.

Key words: Dunkl harmonic oscillator; Sobolev embedding; generalized Hermite functions; Schwartz space.

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