Abstract
INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND - Volume 1, Issue 1, December 2012
Pages: 214-233
The Spectrum of a Matrix Differential Operator
AMAR KUMAR
Category:Engineering, Science and Mathematics
Abstract:
This paper extends the spectral theory of differential operators to encompass matrix differential operators derived from formally self-adjoint matrix differential expressions. Building on the seminal work of Choudhary and Everitt [1], the study establishes conditions under which the spectrum of such operators can be rigorously characterized. By constructing the Green’s matrix and employing variational principles, we derive detailed eigenvalue bounds and investigate the influence of boundary conditions and domain variations on the spectral properties. In particular, we show that the associated differential operator is symmetric and self-adjoint in an appropriate Hilbert space and that its spectrum is discrete under natural conditions. [1, 3, 7].