Sturm-Liouville problems with coupled boundary conditions and Lagrange interpolation series. II (Q2719808)

The paper is a continuation of the study by \textit{W. N. Everitt, G. Schöttler} and \textit{P. L. Butzer} [Rend. Mat. Appl., VII. Ser. 14, No. 1, 87-126 (1994; Zbl 0813.34028)] and by the authors [J. Comput. Anal. Appl. 1, No. 4, 319-347 (1999; Zbl 0944.34019)]. In the first paper, the interpolation analysis is given for Sturm-Liouville boundary value problems with separated boundary selfadjoint conditions. In the second paper, this analysis is given for the case of coupled selfadjoint boundary conditions assuming that all eigenvalues are simple. NEWLINENEWLINENEWLINEThe present paper is concerned with the interpolation analysis of the Sturm-Liouville boundary value problem with coupled boundary conditions for the case when at least one double eigenvalue exists. It is shown that the Kramer analytic kernel [\textit{H. P. Kramer}, J. Math. Phys. 38, 68-72 (1959; Zbl 0196.31702)] can be defined as well as an associated analytic interpolation function generating the Lagrange interpolation series.