Special convolutions on the real line (Q1066399)

The author examines integrals and Steklov's functions of positive order and introduces two concrete convolutions on the real line R. He presents some properties and applications of the convolutions. He also gives an application to fractional calculus. Similar results for periodic functions were given by \textit{P. L. Butzer}, \textit{H. Dyckhoff}, \textit{E. Goehrlich} and \textit{R. L. Stens} [Can. J. Math. 29, 781-793 (1977; Zbl 0357.26003)] and by \textit{P. L. Butzer} and \textit{U. Westphal} [Lect. Notes Math. 457, 116-145 (1975; Zbl 0307.26006)].