Wieners problem for positive definite functions
We study the sharp constant Wn(D) in Wieners inequality for positive definite functions ∫Tn|f|2dx≤Wn(D)|D|-1∫D|f|2dx,D⊂Tn.Wiener proved that W1([- δ, δ]) < ∞, δ∈ (0 , 1 / 2). Hlawka showed that Wn(D) ≤ 2 n, where D is an origin-symmetric convex body. We sharpen Hlawkas estimates for D being t...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/445765 |
| Acceso en línea: | http://hdl.handle.net/2072/445765 |
| Access Level: | acceso abierto |
| Palabra clave: | 51 |
| Sumario: | We study the sharp constant Wn(D) in Wieners inequality for positive definite functions ∫Tn|f|2dx≤Wn(D)|D|-1∫D|f|2dx,D⊂Tn.Wiener proved that W1([- δ, δ]) < ∞, δ∈ (0 , 1 / 2). Hlawka showed that Wn(D) ≤ 2 n, where D is an origin-symmetric convex body. We sharpen Hlawkas estimates for D being the ball δBn and the cube δIn. In particular, we prove that Wn(δBn) ≤ 2 ( 0.401 ⋯ + o ( 1 ) ) n. We also obtain a lower bound of Wn(D). Moreover, for a cube D=1qIn with q= 3 , 4 , … , we obtain that Wn(D) = 2 n. Our proofs are based on the interrelation between Wieners problem and the problems of Turán and Delsarte. © 2017, Springer-Verlag GmbH Deutschland. |
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