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EIGENFUNCTION EXPANSIONS IN Rn.
- Source :
-
Proceedings of the American Mathematical Society . Dec2011, Vol. 139 Issue 12, p4361-4368. 8p. - Publication Year :
- 2011
-
Abstract
- The main goal of this paper is to extend in Rn a result of Seeley on eigenfunction expansions of real analytic functions on compact manifolds. As a counterpart of an elliptic operator in a compact manifold, we consider in Rn a selfadjoint, globally elliptic Shubin type differential operator with spectrum consisting of a sequence of eigenvalues λj, j ϵ N, and a corresponding sequence of eigenfunctions uj, j ϵ N, forming an orthonormal basis of L²(Rn). Elements of Schwartz S(Rn), resp. Gelfand-Shilov S½½ spaces, are characterized through expansions Σj ajuj and the estimates of coefficients aj by the power function, resp. exponential function of λj . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 139
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 65122848
- Full Text :
- https://doi.org/10.1090/S0002-9939-2011-11022-0