Journal of Inequalities and Applications
Volume 2 (1998), Issue 4, Pages 297-306

On the comparison of trigonometric convolution operators with their discrete analogues for Riemann integrable functions

R. J. Nessel and C. Röpsch

Lehrstuhl A für Mathematik, RWTH Aachen, Templergraben 55, Aachen D-52062, Germany

Received 27 June 1997; Revised 12 September 1997

Copyright © 1998 R. J. Nessel and C. Röpsch. 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 note is concerned with a comparison of the approximation-theoretical behaviour of trigonometric convolution processes and their discrete analogues. To be more specific, for continuous functions it is a well-known fact that under suitable conditions the relevant uniform errors are indeed equivalent, apart from constants. It is the purpose of this note to extend the matter to the frame of Riemann integrable functions. To establish the comparison for the corresponding Riemann errors, essential use is made of appropriate stability inequalities.