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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 result 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.
Let $p(cdot): mathbb R^nto(0,1]$ be a variable exponent function satisfying the globally log-Holder continuous condition and $L$ a one to one operator of type $omega$ in $L^2({mathbb R}^n)$, with $omegain[0,,pi/2)$, which has a bounded holomorphic fu
In this paper we prove Hormander-Mihlin multiplier theorems for pseudo-multipliers associated to the harmonic oscillator (also called the Hermite operator). Our approach can be extended to also obtain the $L^p$-boundedness results for multilinear pse
Let $L$ be a one-to-one operator of type $omega$ in $L^2(mathbb{R}^n)$, with $omegain[0,,pi/2)$, which has a bounded holomorphic functional calculus and satisfies the Davies-Gaffney estimates. Let $p(cdot): mathbb{R}^nto(0,,1]$ be a variable exponent
We prove bounds in the local $ L^2 $ range for exotic paraproducts motivated by bilinear multipliers associated with convex sets. One result assumes an exponential boundary curve. Another one assumes a higher order lacunarity condition.
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