1212.5977 (Zouhair Mouayn)

A family of relativistic Bargmann-type transforms attached to Maass
Laplacians on the Poincare disk    [PDF]

Zouhair Mouayn

We construct a set of coherent states through special superpositions of eigenstates of a relativistic pseudoharmonic oscillator. In each superposition the coefficients are chosen to be L2 eingenfunctions of a s-weight Maass Laplacian on the Poincare disk, which are associated with the eigenvalue 4m(s-1 + m), m = 0, 1,...,((s-1) /2).For each integer m the obtained coherent states transform constitutes a of relativistic Bargmann-type transform whose integral kernel is expressed in terms of a special Appel-Kampe de Feriet s hypergeometric function.

View original: http://arxiv.org/abs/1212.5977