International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1980 / Article

Open Access

Volume 3 |Article ID 935357 | https://doi.org/10.1155/S016117128000004X

P. L. Butzer, R. L. Stens, M. Wehrens, "The continous Legendre transform, its inverse transform, and applications", International Journal of Mathematics and Mathematical Sciences, vol. 3, Article ID 935357, 21 pages, 1980. https://doi.org/10.1155/S016117128000004X

The continous Legendre transform, its inverse transform, and applications

Received15 Jan 1979

Abstract

This paper is concerned with the continuous Legendre transform, derived from the classical discrete Legendre transform by replacing the Legendre polynomial Pk(x) by the function Pλ(x) with λ real. Another approach to T.M. MacRobert's inversion formula is found; for this purpose an inverse Legendre transform, mapping L1(+) into L2(1,1), is defined. Its inversion in turn is naturally achieved by the continuous Legendre transform. One application is devoted to the Shannon sampling theorem in the Legendre frame together with a new type of error estimate. The other deals with a new representation of Legendre functions giving information about their behaviour near the point x=1.

Copyright © 1980 Hindawi Publishing Corporation. 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.


More related articles

 PDF Download Citation Citation
 Order printed copiesOrder
Views220
Downloads417
Citations

We are committed to sharing findings related to COVID-19 as quickly as possible. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. Review articles are excluded from this waiver policy. Sign up here as a reviewer to help fast-track new submissions.