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)...

Descripción completa

Detalles Bibliográficos
Autores: Gorbachev, D., Ivanov, V., Tikhonov, S.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
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:2072/445773
Acceso en línea:http://hdl.handle.net/2072/445773
Access Level:acceso abierto
Palabra clave:51
Descripción
Sumario: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.