Uncertainty principles for eventually constant sign bandlimited functions
We study the uncertainty principles related to the generalized Logan problem in Rd. We define λ (f) = sup{ | x| : f(x) > 0} and τ (f) = sup{ | x| : x ∊ supp f} . One of our main results provides the complete solution of the following problem: for a fixed m = 0, 1, 2, . . ., find inf λ (( - 1)...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2020 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositório: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/445773 |
| Acesso em linha: | http://hdl.handle.net/2072/445773 |
| Access Level: | Acceso aberto |
| Palavra-chave: | 51 |
| Resumo: | We study the uncertainty principles related to the generalized Logan problem in Rd. We define λ (f) = sup{ | x| : f(x) > 0} and τ (f) = sup{ | x| : x ∊ supp f} . One of our main results provides the complete solution of the following problem: for a fixed m = 0, 1, 2, . . ., find inf λ (( - 1)mf)τ (f), where the infimum is taken over all nontrivial positive definite bandlimited functions such that ∫Rd | x| 2kf(x) dx = 0 for k = 0, . . ., m - 1 if m ≥ 1. We also obtain the uncertainty principle for bandlimited functions related to the recent result by Bourgain, Clozel, and Kahane. © 2020 Society for Industrial and Applied Mathematics. |
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