We consider the continuous wavelet transform [Formula: see text] associated with the Weinstein operator. We introduce the notion of localization operators for [Formula: see text]. In particular, we prove the boundedness and compactness of localization operators associated with the continuous wavelet transform. Next, we analyze the concentration of [Formula: see text] on sets of finite measure. ...

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We study the one-dimensional random dimer model, with Hamiltonian Hω = ∆ + Vω, where for all x ∈ Z, Vω(2x) = Vω(2x + 1) and where the Vω(2x) are i.i.d. Bernoulli random variables taking the values ±V, V > 0. We show that, for all values of V and with probability one in ω, the spectrum of H is pure point. If V ≤ 1 and V 6= 1/ √ 2, the Lyapounov exponent vanishes only at the two critical energies...

For autonomous mobile robot navigation, localization is an essential capability. Given a equipped with 3D LiDAR sensor, environment map composed of point cloud built beforehand. The thus allowed to localize the position in using sensor scan data. However, sometimes changes due obstacles. Under changing environment, capability might be decreased. this challenge, we propose observation model fram...

We prove that at large disorder, with large probability and for a set of Diophantine frequencies of large measure, Anderson localization in Z is stable under localized time-quasi-periodic perturbations by proving that the associated quasi-energy operator has pure point spectrum. The main tools are the Fröhlich-Spencer mechanism for the random component and the Bourgain-Goldstein-Schlag mechanis...

We study the Schrödinger operator in plane with a step magnetic field function. The bottom of its spectrum is described by infimum lowest eigenvalue band function, for which we establish existence and uniqueness non-degenerate minimum. discuss curvature effects on localization properties ground states, among other applications.

Recent sampling theorems allow for the recovery of operators with bandlimited Kohn-Nirenberg symbols from their response to a single discretely supported identifier signal. The available results are inherently non-local. For example, we show that in order to recover a bandlimited operator precisely, the identifier cannot decay in time nor in frequency. Moreover, a concept of local and discrete ...

We study a quasibound state of a delta -kicked rotor with absorbing boundaries focusing on the nature of the dynamical localization in open quantum systems. The localization lengths xi of lossy quasibound states located near the absorbing boundaries decrease as they approach the boundary while the corresponding decay rates Gamma are dramatically enhanced. We find the relation xi approximately G...