Abel-Gontscharoff interpolation: Continuous, discrete and time scale.
The Abel-Gontscharoff interpolation problem in the real case was introduced in 1935 by J. M. Whittaker and later by V. L. Gontscharoff and P. J. Davis. In the second section of the paper the error analysis for this case (which was first discussed by A. Levin in 1964) is presented and, based on this considerations, tests for the right disfocality as well as disconjugacy for a higher-order equation are obtained. The Abel-Gontscharoff interpolation problem in the discrete case was introduced in 1993 by R. P. Agarwal and B. S. Lalli. The third section of the paper deals with this topic and the major differences from the real case are highlighted. The last section of the paper presents the Abel-Gontscharoff interpolation problem in the time scale case; this topic unifies those topics which appear in the previous two sections.
scientific article; zbMATH DE number 2057261