Profesor Plemelj in reševanje Hilbertovega 21. problema - Hladnik, Milan (Obzornik za matematiko in fiziko, 2024)
It may be less known to the reader that the process of solving Hilbert’s twentyfirst problem did not end in 1908 with the publication of Plemelj’s solution which was considered definitive for almost seventy-five years. In addition to the basic mathematical explanation and Plemelj’s approach to the problem, the article, which avoids complex proofs, briefly describes further research, which at the end of the 20th century led to a surprising turn with the discovery of counterexamples and different conclusions. In the opinion of the author of this paper, the new findings do not diminish the importance of Plemelj’s work and his pioneering role in solving the problem.
Keywords: Fuchsovi sistemi; Hilbertov 21. problem; linearne diferencialne enačbe; matematika; Riemannov problem; singularnosti