Alcune osservazioni sui proiettori armonici su sfere
DOI:
https://doi.org/10.6092/issn.2240-2829/6685Parole chiave:
Complex and quaternionic spheres, SubLaplacian, Laplace-Beltrami operator, Joint spectral projections, Lp eigenfunction bounds, Jacobi polynomials, Zernike polynomialsAbstract
Presentiamo un sunto di alcuni risultati recenti relativi alle proprieta degli operatori di proiezione armonica, che mappano lo spazio delle funzioni a quadrato sommabile sulla sfera unitaria complessa e quaternionica sopra gli autospazi congiunti per l'operatore di Laplace-Beltrami e per un sublaplaciano. Discutiamo, in particolare, analogie e differenze fra il caso reale, quello complesso e quello quaternionico.
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