Some Remarks on Harmonic Projection Operators on Spheres
DOI:
https://doi.org/10.6092/issn.2240-2829/6685Keywords:
Complex and quaternionic spheres, SubLaplacian, Laplace-Beltrami operator, Joint spectral projections, Lp eigenfunction bounds, Jacobi polynomials, Zernike polynomialsAbstract
We give a survey of recent works concerning the mapping properties of joint harmonic projection operators, mapping the space of square integrable functions on complex and quaternionic spheres onto the eigenspaces of the Laplace-Beltrami operator and of a suitably defined subLaplacian. In particular, we discuss similarities and differences between the real, the complex and the quaternionic framework.
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