EXPLICIT FORMULAS AND MEROMORPHIC EXTENSION OF BESSEL FUNCTIONS ON TANGENT SPACES TO NONCOMPACTLY CAUSAL SYMMETRIC SPACES

Salem Ben Saïd (1)

1 IECN - Institut Élie Cartan de Nancy

Assume that $G/H$ is a noncompactly causal symmetric space with restricted root system of the non-exceptional type and the multiplicity of the short roots is even. Using shift operators we obtain explicit formulas for the Bessel function on the tangent space to $G/H$ at the origin. This enable us to investigate the nature and order of the singularities of the Bessel function, and to formulate a conjecture on this matter.

Domaines: Analyse fonctionnelle [math.FA]

Salem Ben Saïd. EXPLICIT FORMULAS AND MEROMORPHIC EXTENSION OF BESSEL FUNCTIONS ON TANGENT SPACES TO NONCOMPACTLY CAUSAL SYMMETRIC SPACES. 2007. ⟨hal-00151973⟩