On completeness of the products of harmonic functions
HTML articles powered by AMS MathViewer
- by A. G. Ramm PDF
- Proc. Amer. Math. Soc. 98 (1986), 253-256 Request permission
Abstract:
Let $L$ be a partial differential operator in ${R^n}$ with constant coefficients. We prove that, under some assumption on $L$, the set of products of the elements of the null-space of $L$ forms a complete set in ${L^p}(D)$, $p \geqslant 1$, where $D$ is any bounded domain. In particular, the products of harmonic functions form a complete set in ${L^p}(D)$, $p \geqslant 1$.References
-
G. Lubarskii, Group theory and its application in physics, Fizmatgiz, Moscow, 1957.
N. Akhiezer, Theory of approximation, Ungar, New York, 1956.
- A. G. Ramm, Scattering by obstacles, Mathematics and its Applications, vol. 21, D. Reidel Publishing Co., Dordrecht, 1986. MR 847716, DOI 10.1007/978-94-009-4544-9
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 98 (1986), 253-256
- MSC: Primary 33A45; Secondary 31B35, 46E30
- DOI: https://doi.org/10.1090/S0002-9939-1986-0854028-0
- MathSciNet review: 854028