"2003 Colloquium on Differential Equations and Applications,
 Maracaibo, Venezuela.
Electronic Journal of Differential Equations,
Conference 13, 2005, pp. 65--74. 

Title: Spectral decomposition theorem for compact 
       self-adjoint operators in prehilbert spaces

Author: Hanzel Larez (Univ. de Los Andes, Trujillo, Venezuela)
 
Abstract: 
 In this paper we found a complete orthonormal system for a prehilbert
 space, in which each element can be expressed as a Fourier series in terms
 of this system. This result is applied to solve second order differential
 equations with initial or boundary conditions. In particular, it is
 applied to Dirichlet problem and to Neumann problem.

Published May 30, 2005.
Math Subject Classifications: 34L05, 47B07
Key Words: Hilbert spaces; prehilbert;  self-adjoint; super-injective;
           compact operator; complete orthonormal systems.