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Converse theorems in the theory of approximate integration |
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| Authors: | D P Dryanov Q I Rahman G Schmeisser |
| Institution: | 1. Institute of Mathematics with Computer Center, Bulgarian Academy of Sciences, P.O. Box 373, 1090, Sofia, Bulgaria 2. Département de mathématiques et de statistique, Université de Montréal, Succursale A, C.P. 6128, H3C 3J7, Montréal, Québec, Canada 3. Mathematisches Institut, Universit?t Erlangen-Nürnberg, Bismarckstrasse 1 1/2, D-8520, Erlangen, F.R.G. |
| Abstract: | We characterize certain function classes in terms of the remainder in the quadrature formula \(\int_{ - \infty }^\infty {f(x)dx = (\pi /\sigma )\sum\nolimits_{v = - \infty }^\infty {f(v\pi /\sigma ) + R_\sigma f]} } \) . In the process, we prove a generalization of the famous theorem of Paley and Wiener about entire functions of exponential type belonging toL 2 on the real line. |
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