ترغب بنشر مسار تعليمي؟ اضغط هنا

Uncertainty principles for eventually constant sign bandlimited functions

64   0   0.0 ( 0 )
 نشر من قبل Dmitry Gorbachev
 تاريخ النشر 2019
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

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.



قيم البحث

اقرأ أيضاً

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 ${(fastvarphi_u)(lambda), lambdainLambda, uin I}$.
120 - Elena A. Lebedeva 2014
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 minimization problem for a non-periodic (Heisenberg) uncertainty constant is studied.
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 lt is applied to get a uniqueness result for functions with spectrum supported on sufficiently flat sets. One corollary is that a function with spectrum in an annulus of a given thickness can be bounded, in $L^2$-norm, from above by its restriction to any open GCC set, independent of the radius of the annulus. This result is applied to the energy decay rates for damped fractional wave equations.
116 - Kai Diethelm 2015
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 s $alpha in (0,1)$ with starting point $a$ of this function do not have a change of sign there. In contrast to what is occasionally conjectured, it not sufficient if the Caputo derivatives have a constant sign for a few values of $alpha in (0,1)$ only.
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 uity function that is nowhere vanishing. It is less clear, however, what can be said in terms of unique phase-retrievability when the ambiguity function of the underlying window vanishes on some of the time-frequency plane. In this short note, we demonstrate that by considering signals in Paley-Wiener spaces, it is possible to prove new uniqueness results for STFT phase retrieval. Among those, we establish a first uniqueness theorem for STFT phase retrieval from magnitude-only samples in a real-valued setting.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا