International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 3, Pages 465-484
doi:10.1155/S0161171293000584

Projection solutions of Frobenius-Perron operator equations

Jiu Ding1,2 and Tien Tien Li1,2

1Department of Mathematics, University of Southern Mississippi, Hattiesburg 39406, MS, USA
2Department of Mathematics, Michigan State University, East Lansing 48824, MI, USA

Received 10 December 1990; Revised 2 June 1991

Copyright © 1993 Jiu Ding and Tien Tien Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We construct in this paper the first order and second order piecewise polynomial finite approximation schemes for the computation of invariant measures of a class of nonsingular measurable transformations on the unit interval of the real axis. These schemes are based on the Galerkin's projection method for L1-spaces and are proved to be convergent for the class of Frobenius-Perron operators.