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The Green operator ${\mathrm{\Gamma }}^{(n)}$ of the differential problem (having as eigenvalues the ${\lambda }_h^{(n)}$'s introduced in Nota I, is constructed. It is shown that the orthogonal invariant converges by decreasing to the corresponding orthogonal invariant ${ℐ}_1^s({\mathrm{\Gamma }}^{(n)})$ of the eigenvalue problem considered in Nota I and the approximation error is estimated.

The lower bounds ${\lambda }_h^{(n)}$ to the eigenvalues ${\lambda }_h$ of the problem considered in Nota I, are obtained as zeroes of a trascendental function represented by a $2n\times 2n$ determinant. A procedure for the computation of this determinant, by means of recursion formulas, is given.

The eigenvalue problem (1) is considered and for any eigenvalue ${\lambda }_k$ an increasing sequence ${\lambda }_h^{(n)}$ converging to ${\lambda }_k$ is constructed. The approximation error ${\lambda }_h-{\lambda }_h^{(n)}$is estimated. The ${\lambda }_h^{(n)}$ are obtained as eigenvalues of a differential equation with piecewise constant coefficients.