Closedness and Normal Solvability of an Operator Generated by a Degenerate Linear Differential Equation with Variable Coefficients

@inproceedings{Zhuk2008ClosednessAN,
title={Closedness and Normal Solvability of an Operator Generated by a Degenerate Linear Differential Equation with Variable Coefficients},
author={Sergiy M. Zhuk},
year={2008}
}

we prove that its graph is closed and determine the adjoint operator D∗ : W ′ 2 ⊂ L2 × R → L2 . For elements of the linear manifolds W2 and W ′ 2 , we propose an analog of the formula of integration by parts. We establish a criterion for the existence of a pseudosolution of the operator equation Dx(·) = (f(·), f0) and formulate sufficient conditions for the normal solvability of the operator D in terms of relations for blocks of the matrix C(t). The results obtained are illustrated by examples.