Completeness of generalized eigenfunction systems of in nite-dimensional Hamiltonian operators and its application in Elasticity

Abstract

By using the structural characteristics of the infinite-dimensional Hamiltonian operators, a necessary and sufficient condition is given for generalized eigenfunction systems to be complete in the sense of Cauchy principal value. The above function systems consist of the eigenfunction and Jordan eigenfunction of the operators. Moreover, the result is applied to plate bending problems. The related conclusion offers a theoretical guarantee for the separation of variables in Hamiltonian system (the new systematic methodology for theory of elasticity).