STUDY OF SPECTRAL THEORY AND EIGEN FUNCTIONS EXPENSIONS FOR A PAIR OF SECOND ORDER MATRIX DIFFERENTIAL EQUATION
RABISH KUMAR
Research Scholar, University Department of Mathematics, T. M. B. University, Bhagalpur , IN
AMAR KUMAR
Research Scholar, University Department of Mathematics, T. M. B. University, Bhagalpur , IN
Keywords: Matrix differential operator, convergence theorem, bounded variation.
Abstract
The present paper concerned with spectral theory and eigen functions expansions for a pair of second order matrix differential equation. The theory of eigenfunction expansions associated with the second order differential equations dates as far back as the time of Sturm and Liouville. The discussion on the systems of simultaneous differential equations of first orderhowever, appears to have been initiated by Bocher in 1902.
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