Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On completeness of the products of harmonic functions


Author: A. G. Ramm
Journal: Proc. Amer. Math. Soc. 98 (1986), 253-256
MSC: Primary 33A45; Secondary 31B35, 46E30
MathSciNet review: 854028
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] G. Lubarskii, Group theory and its application in physics, Fizmatgiz, Moscow, 1957.
  • [2] N. Akhiezer, Theory of approximation, Ungar, New York, 1956.
  • [3] A. G. Ramm, Scattering by obstacles, Mathematics and its Applications, vol. 21, D. Reidel Publishing Co., Dordrecht, 1986. MR 847716 (87k:35197)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 33A45, 31B35, 46E30

Retrieve articles in all journals with MSC: 33A45, 31B35, 46E30


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0854028-0
PII: S 0002-9939(1986)0854028-0
Article copyright: © Copyright 1986 American Mathematical Society