ﻻ يوجد ملخص باللغة العربية
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},}to 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.
For a wide family of even kernels ${varphi_u, uin I}$, we describe discrete sets $Lambda$ such that every bandlimited signal $f$ can be reconstructed from the space-time samples ${(fastvarphi_u)(lambda), lambdainLambda, uin I}$.
An inequality refining the lower bound for a periodic (Breitenberger) uncertainty constant is proved for a wide class of functions. A connection of uncertainty constants for periodic and non-periodic functions is extended to this class. A particular
In this paper, we study forms of the uncertainty principle suggested by problems in control theory. First, we prove an analogue of the Paneah-Logvinenko-Sereda Theorem characterizing sets which satisfy the Geometric Control Condition (GCC). This resu
It is well known that a continuously differentiable function is monotone in an interval $[a,b]$ if and only if its first derivative does not change its sign there. We prove that this is equivalent to requiring that the Caputo derivatives of all order
We consider the problem of phase retrieval from magnitudes of short-time Fourier transform (STFT) measurements. It is well-known that signals are uniquely determined (up to global phase) by their STFT magnitude when the underlying window has an ambig