SPECTRAL THEORY OF EIGENFUNCTION EXPANSION WITH SECOND ORDER DIFFERENTIAL EQUATION

Abstract

In this paper the spectral asymptotic behaviour of the spectrum for Spectra of differential equations in particulars, challenges the common notion that one must limit the complexity of the expansion used when variables are taken in finite or infinite intervals. The spectral theory of eigenfunction expansion associated with second-order differential equations goes at least as far baok as the time of Weyl. Wely used the method of integral equation in his discussions, but in the forties Ticharah used the theory of complex variable methods to generalize some of Weyl's results. He made a systematic study of the theory of eigenfunction expansions till his death in early 1963.