On spectral expansions of piecewise smooth functions depending on the geodesic distance

We consider the expansion of a piecewise smooth function depending on the geodesic distance to some point in the eigenfunctions of the Beltrami-Laplace operator on an n -dimensional symmetric space of rank 1. We show that if the expansion converges at this point, then the function must have continuo...

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Bibliographic Details
Published in:Differential equations 2010-06, Vol.46 (6), p.827-839
Main Author: Alimov, Sh. A.
Format: Article
Language:English
Subjects:
Belts
Derivatives
Difference and Functional Equations
Differential equations
Eigenfunctions
Eigenvalues
Geodetics
Laplace transforms
Mathematics
Mathematics and Statistics
Operators
Ordinary Differential Equations
Partial Differential Equations
Spectra
Spheres
Studies
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Summary:We consider the expansion of a piecewise smooth function depending on the geodesic distance to some point in the eigenfunctions of the Beltrami-Laplace operator on an n -dimensional symmetric space of rank 1. We show that if the expansion converges at this point, then the function must have continuous derivatives up to and including the order ( n − 3)/2.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266110060078