相关论文: Finite propagation speed and kernel estimates for …
Maximal estimates for Schr\"odinger means and convergence almost everywhere of sequences of Schr\"odinger means are studied.
We prove uniform Sobolev estimates for the resolvent of Schr\"odinger operators with large scaling-critical potentials without any repulsive condition. As applications, global-in-time Strichartz estimates including some non-admissible…
We study the scattering problem, the Sturm-Liouville problem and the spectral problem with periodic or skew-periodic boundary conditions for the one-dimensional Schr\"odinger equation with an $n$-cell (finite periodic) potential. We give…
We prove qualitatively sharp heat kernel bounds in the setting of Fourier-Bessel expansions when the associated type parameter $\nu$ is half-integer. Moreover, still for half-integer $\nu$, we also obtain sharp estimates of all kernels…
Explicit formulas for the analytic extensions of the scattering matrix and the time delay of a quasi-one-dimensional discrete Schr\"odinger operator with a potential of finite support are derived. This includes a careful analysis of the…
For integral kernels on space-time we indicate a class of nonnegative Schr\"odinger perturbations which produce comparable integral kernels.
Exact Hausdorff dimensions are computed for singular continuous components of the spectral measures of a class of Schr\"odinger operators in bounded intervals.
We consider the Cauchy problem for the nonlinear Schr\"odinger equation on the whole space. After introducing a weaker concept of finite speed of propagation, we show that the concatenation of initial data gives rise to solutions whose time…
The aim of these notes is to describe some recent results concerning dispersive estimates for principally normal pseudodifferential operators. The main motivation for this comes from unique continuation problems. Such estimates can be used…
We characterize the Schwartz kernels of pseudodifferential operators of Shubin type by means of an FBI transform. Based on this we introduce as a generalization a new class of tempered distributions called Shubin conormal distributions. We…
We study the distribution of the eigenvalues inside of the essential spectrum for discrete one-dimensional Schr\"odinger operators with potentials of Coulomb type decay.
We use B\'{e}zout's theorem and Bernstein-Khovanskii-Kushnirenko theorem to analyze the level sets of the extrema of the spectral band functions of discrete periodic Schr\"odinger operators on $\mathbb{Z}^2$. These approaches improve upon…
We view sequential design as a model selection problem to determine which new observation is expected to be the most informative, given the existing set of observations. For estimating a probability distribution on a bounded interval, we…
We investigate the kernels of the transformation operators for one-dimensional Schroedinger operators with potentials, which are asymptotically close to Bohr almost periodic infinite-gap potentials.
Based on the recent work \cite{KKK} for compact potentials, we develop the spectral theory for the one-dimensional discrete Schr\"odinger operator $$ H \phi = (-\De + V)\phi=-(\phi_{n+1} + \phi_{n-1} - 2 \phi_n) + V_n \phi_n. $$ We show…
It is known in scattering theory that the minimal velocity bound plays a conclusive role in proving the asymptotic completeness of the wave operators. In this study, we prove the minimal velocity bound and other important estimates for the…
The use of second order boundary kernels for distribution function estimation was recently addressed in the literature (C. Tenreiro, 2013, Boundary kernels for distribution function estimation, REVSTAT-Statistical Journal, 11, 169-190). In…
We study integral estimates of maximal functions for Schr\"odinger means.
In this note we show the optimal gradient estimate for heat kernels of stable-like operators by providing a counterexample.
We study the spectral inequalities of Schr\"odinger operator in the whole space for different potentials, which can be power growth or continuously vanishing at infinity. The spectral inequalities quantitatively depend on the density of the…