International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 2, Pages 355-362

Operational calculs for the continuous Legendre transform with applications

E. Y. Deeba1 and E. L. Koh2

1Department of Applied Mathematical Sciences, University of Houston-Downtown, Houston 77002, Texas, USA
2Department of Mathematics and Statistics, University of Regina, Regina S4S 0A2, Saskatchewan, Canada

Received 13 June 1988; Revised 1 September 1988

Copyright © 1989 E. Y. Deeba and E. L. Koh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper develops an operational calculus for the continuous Legendre transform introduced and studied by Butzer, Stens and Wehrens [1]. It is an extension of the work done by Churchill et al [2], [31 for the discrete case. In particular, a differentiation theorem and a convolution theorem are proved and the results are applied to the solution of some boundary value problems.