SPECTRAL ASYMPTOTIC BEHAVIOUR OF THE SPECTRUM FOR ZEROS OF EIGEN FUNCTIONS

Abstract

In this paper the spectral asymptotic behaviour of the spectrum for self-adjoint matrix is obtained in zeros of Eigen functions and related works and 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. Zeros of Eigen functions and related works It appears that the theory on the zeros of solutions of second order differential equations in a given interval was dealt with first by Sturm , a complete account of which and its subsequent development may be found in a Paris monograph by Bocher (1917). We however outline some of the developments of the theory in brief after the forties.