## 3. The Hilbert space of the displacement fieldLet be a function space whose elements are and in which the inner product is defined as where the integration is over the volume of the star. on is self adjoint, . There follows the eigenvalue problem where is the eigenfrequency of an
oscillation mode, is its eigendisplacement
vector, and The set is also complete and may serve as a basis for . See Dixit et al. (1980). Thus, any may be expanded in a unique way in terms of . Numerical values of for hypothetical or actual star models are abundant in the astronomical literature of seventies and eighties. © European Southern Observatory (ESO) 1997 Online publication: June 30, 1998 |