
%0 Journal Article
%A Mason, DP 
%T The Vlasov?Maxwell Operators in Self-adjoint Form
%J Australian Journal of Physics
%D 1973/06/01
%V 26
%N 3
%P 301-314
%K 
%R https://doi.org/10.1071/PH730301
%U https://www.publish.csiro.au/paper/PH730301 
%X A systematic method for obtaining the scalar product with respect to which a given Vlasov-Maxwell operator is self-adjoint is illustrated by considering the operator introduced by Shure (1964) to describe one-dimensional longitudinal oscillations in a bounded plasma. By separation of variables the problem is reduced to the solution of a singular integral equation for the weight function of the scalar product. The solution of this equation is not explicit but is in the form of a simple linear Fredholm integral equation of the second kind which is easily solved. The method should be applicable to similar operators in this field. 
