Uncertainty Principles for Eventually Constant Sign Bandlimited Functions
Uncertainty Principles for Eventually Constant Sign Bandlimited Functions
复制标题
最终恒定符号带限函数的不确定性原理
DOI：
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发表时间：
2019
影响因子：
2
通讯作者：
S. Tikhonov
中科院分区：
文献类型：
--
作者：
D. Gorbachev;V. Ivanov;S. Tikhonov
We study the uncertainty principles related to the generalized Logan problem in $mathbb{R}^{d}$. Our main result provides the complete solution of the following problem: for a fixed $min mathbb{Z}_{+}$, find [ sup{|x|colon (-1)^{m}f(x)>0}cdot sup {|x|colon xin mathrm{supp},widehat{f},} o inf, ] where the infimum is taken over all nontrivial positive definite bandlimited functions such that $int_{mathbb{R}^d}|x|^{2k}f(x),dx=0$ for $k=0,dots,m-1$ if $mge 1$.
We also obtain the uncertainty principle for bandlimited functions related to the recent result by Bourgain, Clozel, and Kahane.
We study the uncertainty principles related to the generalized Logan problem in $mathbb{R}^{d}$. Our main result provides the complete solution of the following problem: for a fixed $min mathbb{Z}_{+}$, find [ sup{|x|colon (-1)^{m}f(x)>0}cdot sup {|x|colon xin mathrm{supp},widehat{f},} o inf, ] where the infimum is taken over all nontrivial positive definite bandlimited functions such that $int_{mathbb{R}^d}|x|^{2k}f(x),dx=0$ for $k=0,dots,m-1$ if $mge 1$.
We also obtain the uncertainty principle for bandlimited functions related to the recent result by Bourgain, Clozel, and Kahane.