Coherent states on the unit ball of Cn and asymptotic expansion of their associated covariant symbol

Article type: Research Article

Authors: Díaz-Ortíz, Erik I.^{; *}

Affiliations: CONACYT, Universidad Pedagógica Nacional, Unidad 201, Oaxaca, México. E-mail: eidiazor@conacyt.mx

Correspondence: [*] Corresponding author. E-mail: eidiazor@conacyt.mx.

Abstract: Starting from a complete family for the unit sphere Sn in the complex n-space Cn (whose elements are coherent states attached to the Barut–Girardello space), we obtain an asymptotic expansion for the associated Berezin transform. The proof involves the computation of the asymptotic behaviour of functions in the complete family. Furthermore, in an analogous manner (slightly weaker) we obtain the asymptotic expansion of the covariant symbol of a pseudo-differential operator on L2(Sn).

Keywords: Holomorphic space, Berezin transform, Bessel function, asymptotic approximation, semiclassical pseudo-differential operator, coherent states

DOI: 10.3233/ASY-201604

Journal: Asymptotic Analysis, vol. 121, no. 3-4, pp. 307-333, 2021