Spherical Functions on SO0(p, q)/ SO(p) × SO(q)

Sawyer, P.

Canadian mathematical bulletin, Tome 42 (1999) no. 4, pp. 486-498

Résumé

An integral formula is derived for the spherical functions on the symmetric space ${G}/{K\,=\,{\text{S}{{\text{O}}_{0}}\left( p,\,q \right)}/{\text{SO}\left( p \right)\,\times \,\text{SO}\left( q \right)}\;}\;$ . This formula allows us to state some results about the analytic continuation of the spherical functions to a tubular neighbourhood of the subalgebra a of the abelian part in the decomposition $G\,=\,KAK$ . The corresponding result is then obtained for the heat kernel of the symmetric space ${\text{S}{{\text{O}}_{0}}\left( p,\,q \right)}/{\text{SO}\left( p \right)\,\times \,\text{SO}\left( q \right)}\;$ using the Plancherel formula.In the Conclusion, we discuss how this analytic continuation can be a helpful tool to study the growth of the heat kernel.

Détail

DOI : 10.4153/CMB-1999-056-5

Mots-clés : 33C55, 17B20, 53C35

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