Homeomorphism results and minimax type theorems for sum of translates functions

Abstract: Minimax and maximin type problems are investigated for sum of translates of concave kernel functions. A homeomorphism type theorem is shown for difference of local maxima. As an immediate application, Lagrange interpolation for algebraic polynomials and trigonometric polynomials can be deduced. Furthermore, one can generalize a theorem of Mycielsi and Paszkowski, and some results of Bojanov. We also investigate minimax problems for such sums of translates and we obtain a general minimax result in which equioscillating, minimax and maximin configurations are related to each other. The presentation is based on joint work with Balint Farkas and Szilard Revesz and is also available as Online First at https://doi.org/10.1007/s13163-023-00461-6