Cesaro asymptotic equipartition of energy in the coupled case

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.

Keywords

• Cesaro asymptotic equipartition of energy
• selfadjoint operator matrices
• direct sum Hilbert space
• evolution equations
• initial boundary value problem
• coupled boundary condition.