Operational calculus for the continuous Legendre transform with applications (Q1120102)

The authors develop an operational calculus for the continuous Legendre transform introduced and studied by \textit{P. L. Butzer}, \textit{P. L. Stens} and \textit{M. Wehrens} [Int. J. Math. Math.Sci. 3, No.1, 47-67 (1980; Zbl 0447.44001)]. It is an extension of the work done by \textit{R. V. Churchill} [J. Math. Phys. 33, 165-178 (1954; Zbl 0055.095)] and \textit{R. V. Churchill} and \textit{C.-L. Dolph} [Proc. Amer. Math. Soc., 5, 93-100 (1954; Zbl 0055.094)] for the discrete case. The authors prove a differentiation theorem and a convolution theorem and apply the results to the solution of some boundary value problems.