Geodesic
A Generalization of the Fundamental Theorem of Spherical Harmonic Theory
Contemporary Mathematics. Fundamental Directions, Theory of functions, Tome 25 (2007), pp. 102-105
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We consider a first kind boundary value problem for a selfadjoint differential operator with constant coefficients on a domain in $\mathbb R^n$ bounded by an ellipsoid; boundary conditions are defined by an arbitrary polynomial of degree $N$. It is proved that the solution of the problem is again a polynomial of degree $\le N$. 
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S. M. Nikol'skii. A Generalization of the Fundamental Theorem of Spherical Harmonic Theory. Contemporary Mathematics. Fundamental Directions, Theory of functions, Tome 25 (2007), pp. 102-105. http://geodesic.mathdoc.fr/item/CMFD_2007_25_a8/

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