Geodesic
A Generalization of the Fundamental Theorem of Spherical Harmonic Theory
Contemporary Mathematics. Fundamental Directions, Theory of functions, Tome 25 (2007), pp. 102-105

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $\le N$. 
@article{CMFD_2007_25_a8,
     author = {S. M. Nikol'skii},
     title = {A {Generalization} of the {Fundamental} {Theorem} of {Spherical} {Harmonic} {Theory}},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {102--105},
     publisher = {mathdoc},
     volume = {25},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2007_25_a8/}
}
TY  - JOUR
AU  - S. M. Nikol'skii
TI  - A Generalization of the Fundamental Theorem of Spherical Harmonic Theory
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2007
SP  - 102
EP  - 105
VL  - 25
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2007_25_a8/
LA  - ru
ID  - CMFD_2007_25_a8
ER  - 
%0 Journal Article
%A S. M. Nikol'skii
%T A Generalization of the Fundamental Theorem of Spherical Harmonic Theory
%J Contemporary Mathematics. Fundamental Directions
%D 2007
%P 102-105
%V 25
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2007_25_a8/
%G ru
%F CMFD_2007_25_a8
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/