Related papers: Propagation estimates in the one-commutator theory
A novel approach is developed for analytic orbit propagation based on asymptotic expansion with respect to a small perturbative acceleration. The method improves upon existing first order asymptotic expansions by leveraging on linear…
In this paper we study systems of $N$ uniformly expanding coupled maps when $N$ is finite but large. We introduce self-consistent transfer operators that approximate the evolution of measures under the dynamics, and quantify this…
Channel properties influence the development of wireless communication systems. Unlike wired channels that are stationary and predictable, radio channels are extremely random and dont offer easy analysis. A Radio Propagation Model (RPM),…
Conditions for existence, uniqueness and stability of bunch steady states are considered. For the existence uniqueness problem, simple algebraic equations are derived, showing the result both for the action and Hamiltonian domain…
We find the laws for the spreading of the spatial widths (parallel and transverse to the direction of average motion) of the relativistic position probability density for a massive, spinless particle. We find that when the momentum width of…
Unfolding problems often arise in the context of statistical data analysis. Such problematics occur when the probability distribution of a physical quantity is to be measured, but it is randomized (smeared) by some well understood process,…
We use the methods of commutator and fundamental solutions to establish averaging lemmas and hypoelliptic estimates for purely kinetic transport equations. Assuming certain amount of velocity regularity for solutions, we extend our analysis…
In this note we investigate propagation of smallness properties for solutions to heat equations. We consider spectral projector estimates for the Laplace operator with Dirichlet or Neumann boundary conditions on a Riemanian manifold with or…
A hybrid observer is described for estimating the state of a system of the form dot x=Ax, y_i=C_ix, i=1,...,m. The system's state x is simultaneously estimated by m agents assuming agent i senses y_i and receives appropriately defined data…
We give an alternative proof of several sharp commutator estimates involving Riesz transforms, Riesz potentials, and fractional Laplacians. Our methods only involve harmonic extensions to the upper half-space, integration by parts, and…
Estimates are given of the time scales which govern spreading of a coherent state wave packet. The estimates, based on dimensional analysis, suggest that spreading should be small for coherent states with average angular momentum of order…
The task of position and velocity estimation of a moving transmitter (with either a known or unknown frequency) is a common problem arising in many different application domains. Based on the Doppler effect, this work presents a direct…
We study spectral properties of convolution operators $\mathcal L$ and their perturbations $H=\mathcal L+v(x)$ by compactly supported potentials. Results are applied to determine the front propagation of a population density governed by…
This paper is the third part of our study started with Cattiaux, Le\'{o}n and Prieur [Stochastic Process. Appl. 124 (2014) 1236-1260; ALEA Lat. Am. J. Probab. Math. Stat. 11 (2014) 359-384]. For some ergodic Hamiltonian systems, we obtained…
This work is devoted to radiative transfer equations with long-range interactions. Such equations arise in the modeling of high frequency wave propagation in random media with long-range dependence. In the regime we consider, the singular…
We consider an abstract non-negative self-adjoint operator $H$ on an $L^2$-space. We derive a characterization for the restriction estimate $\| dE_H(\lambda) \|_{L^p \to L^{p'}} \le C \lambda^{\frac{d}{2}(\frac{1}{p} - \frac{1}{p'}) -1}$ in…
In many radar scenarios, the radar target or the medium is assumed to possess randomly varying parts. The properties of a target are described by a random process known as the spreading function. Its second order statistics under the WSSUS…
We introduce a novel notion of {\it local spectral gap} for general, possibly infinite, measure preserving actions. We establish local spectral gap for the left translation action $\Gamma\curvearrowright G$, whenever $\Gamma$ is a dense…
The main Theorem of Jain et al.[Jain, K., Singh, S., and Sharma, S. (2011), Re- stricted estimation in multivariate measurement error regression model; JMVA, 102, 2, 264-280] is established in its full generality. Namely, we derive the…
We report a detailed and systematic numerical study of wave propagation through a coherently amplifying random one-dimensional medium. The coherent amplification is modeled by introducing a uniform imaginary part in the site energies of the…