SOME HARMONIC ANALYSIS ON THE QUATERNIONIC SPHERE
VALENTINA CASARINO
` DEGLI STUDI DI PADOVA
UNIVERSITA
In this talk, we present some results, obtained in collaboration with V´eronique Fischer
(Imperial College, Londra) and Paolo Ciatti (Universit`a di Padova), concerning the harmonic analysis on the unit sphere S 4n−1 in Hn . We shall discuss, in particular, some elliptic
and sub elliptic operators, acting on S 4n−1 , providing optimal bounds for the associated
spectral projectors. These estimates turn out to be quite different from those known for
the real and the complex sphere. Our work is based on the analysis carried out by K. D.
Johnson and N. R. Wallach [JW].
References
[JW]
K. D. Johnson and N. R. Wallach, Composition series and intertwining operators for the spherical
principal series. I, Trans. Amer. Math. Soc., 229 (1977), 137-173.
E-mail address: valentina.casarino@unipd.it
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