On the distribution of the eigenvalues of a matrix differential operator

N K CHAKRAVARTY, PRABIR KUMAR SEN GUPTA

Abstract


The paper deals with the nature of the spectrum associated with the type of second-ordcr matrix differential operator with catain boundary conditions. It is found that under certain conditions. satisfied by the co-efficients of the differential system, the spectrum is discrete. Some results are then obtained giving distributions of the eigenvalues on the real axis. The method employed depends, among others upon some of the ideas and techniques of E. C. Titchmarsh.

Keywords


Differential operator; eigenvalue problem; Hubert space; Dirichlet (Neumann) problem Spectrum-discrete; continuous; point continuous; Green's matrix; micromorphic function; pseudomonotonic:; variation of the eigenvalues; distribution of the eigenvalue

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