Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 70, pp. 1-11.

Title: Cesaro asymptotic equipartition of energy in the coupled case

Author: Stefan Boller (Univ. Leipzig, Leipzig, Germany)

Abstract: 
    It is well known from earlier results that certain types of selfadjoint
    operators, e.g. operators allowing a representation as operator matrices,
    show equipartition of energy. In this paper we examine the question
    whether there are more selfadjoint operators showing equipartition of
    energy in the Cesaro mean. For this purpose we proof a necessary and
    sufficient criterion for equipartition of energy and use this criterion to
    show equipartition for a system of partial differential equations with a
    coupled boundary condition. 

Submitted March 14, 2000. Published November 20, 2000.
Math Subject Classifications: 36G10, 47B25, 47D03, 34D05.
Key Words: Cesaro asymptotic equipartition of energy; selfadjoint operator 
           matrices; direct sum Hilbert space; evolution equations; 
           initial boundary value problem; coupled boundary condition.