Journal of Inequalities and Applications
Volume 1 (1997), Issue 2, Pages 149-164

Hermite interpolation and an inequality for entire functions of exponential type

Georgi R. Grozev1 and Qazi I. Rahman2

1Numetrix Ltd., 655 Bay Street, Suite 1200, Ontario, Toronto M5G 2K4, Canada
2Département de Mathématiques et de Statistique, Université de Montréal, Québec, Montréal H3C 3J7, Canada

Received 11 September 1996

Copyright © 1997 Georgi R. Grozev and Qazi I. Rahman. 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.


Let c[0,1),p>0. It is shown that if f is an entire function of exponential type cmπ and n=μ=0m1|f(μ)(λn)|p<, where {λn}n is a sequence of real numbers satisfying |λnn|Δ<, |λn+uλn|δ>0 for u0, then |f(x)|pdx<Bn=μ=0m1|f(μ)(λn)|p, where B depends only on c,p,Δ, and δ. A sampling theorem for irregularly spaced sample points is obtained as a corollary. Our proof of the main result contains ideas which help us to obtain an extension of a theorem of R.J. Duffin and A.C. Schaeffer concerning entire functions of exponential type bounded at the points of the above sequence {λn}n .