This paper gives optimal order error estimates for the approximation of the spectral properties of a variant of the shallow water equations by a finite element procedure recently proposed by Platzman. General results on the spectral approximation of unbounded, selfadjoint operators are also given in this paper.

We study degenerate hypoelliptic Ornstein-Uhlenbeck operators in L spaces with respect to invariant measures. The purpose of this article is to show how recent results on general quadratic operators apply to the study of degenerate hypoelliptic Ornstein-Uhlenbeck operators. We first show that some known results about the spectral and subelliptic properties of Ornstein-Uhlenbeck operators may be...

BRANKO CURGUS and BRANKO NAJMAN Deenitizable operators in Krein spaces have spectral properties similar to those of selfadjoint operators in Hilbert spaces. A suucient condition for deenitizability of a selfadjoint operator A with a nonempty resolvent set (A) in a Krein space (H; j ]) is the niteness of the number of negative squares of the form Axjy] (see 10, p. 11]). In this note we consider ...