Related papers: Uniform resolvent estimates for the discrete Schr\…

We prove smoothing estimates for Schr\"odinger equations $i\partial_t \phi+\partial_x (a(x) \partial_x \phi) =0$ with $a(x)\in \mathrm{BV}$, the space of functions with bounded total variation, real, positive and bounded from below. We then…

This paper applies Hermite function techniques to give elementary proofs of Kato type smoothing estimates for the Schr\"odinger equation with quadratic potential in R^n+1. This is equivalent to proving a uniform L^2(R^n) to L^2(R^n)…

We discuss bilinear estimates of tempered distributions in the Fourier restriction spaces for the two-dimensional Sch\"odinger equation whose principal part is the d'Alembertian. We prove that the bilinear estimates hold if and only if the…

We prove and apply two theorems: First, a quantitative, scale-free unique continuation estimate for functions in a spectral subspace of a Schr\"odinger operator on a bounded or unbounded domain, second, a perturbation and lifting estimate…

In this paper, we investigate Strichartz estimates for discrete linear Schr\"odinger and discrete linear Klein-Gordon equations on a lattice $h\mathbb{Z}^d$ with $h>0$, where $h$ is the distance between two adjacent lattice points. As for…

We derive the dispersion decay for solutions of the 1D discrete Schroedinger and wave equations. Based on previous works, we weaken the conditions on potentials.

In this paper we study $L^p-L^r$ estimates of both extension operators and averaging operators associated with the algebraic variety $S=\{x\in {\mathbb F}_q^d: Q(x)=0\}$ where $Q(x)$ is a nondegenerate quadratic form over the finite field…

An improved lower bound is given for the decay of conical averages of Fourier transforms of measures, for cones of dimension $d \geq 4$. The proof uses a weighted version of the broad restriction inequality, a narrow decoupling inequality…

In this paper, we shall prove the uniform sharp $L^p$ decay estimates for a class of oscillatory integral operators with polynomial phases. By this one-dimensional result, we can use the rotation method to obtain uniform sharp $L^p$…

We characterize the set of diagonals of the unitary orbit of a self-adjoint operator with three points in the spectrum. Our result gives a Schur-Horn theorem for operators with three point spectrum analogous to Kadison's result for…

A global solution of the Schr\"odinger equation, obtained recently within the wave operator formalism for explicitly time-dependent Hamiltonians [J. Phys. A: Math. Theor. 48, 225205 (2015)], is generalized to take into account the case of…

We show that it is possible to construct a lattice Schroedinger functional for standard Wilson fermions, where the expectation values of ${\cal R}_5$-even operators are O($a$) improved, up to terms coming from the boundaries.

We consider a version of the stationary phase method in one dimension of A. Erd\'elyi, allowing the phase to have stationary points of non-integer order and the amplitude to have integrable singularities. After having completed the original…

We prove $L^p-L^{p^\prime}$ boundedness of spectral projections and the resolvent of the Laplace-Beltrami operator on Damek-Ricci spaces with the explicit norms in terms of the spectral parameter. To prove these results we established…

I present an example of a discrete Schr"odinger operator that shows that it is possible to have embedded singular spectrum and, at the same time, discrete eigenvalues that approach the edges of the essential spectrum (much) faster than…

We give a bound on the number of isolated, essential singularities of determinantal quartic surfaces in 3-space. We also provide examples of different configurations of real singularities on quartic surfaces with a definite Hermitian…

We consider some compact non-selfadjoint perturbations of fibered one-dimensional discrete Schr\"odinger operators. We show that the perturbed operator exhibits finite discrete spectrum under suitable\- regularity conditions.

We prove a sharp resolvent estimate in scale invariant norms of Amgon--H\"{o}rmander type for a magnetic Schr\"{o}dinger operator on $\mathbb{R}^{n}$, $n\ge3$\begin{equation*} L=-(\partial+iA)^{2}+V \end{equation*}with large potentials…

We prove that if a solution of the discrete time-dependent Schr\"odinger equation with bounded real potential decays fast at two distinct times then the solution is trivial. For the free Shr\"odinger operator and for operators with…

The main result of this paper is, that if we suppose that a function is absolutely continuous and uniformly H\"older continuous and that its finite difference function does not oscillate infinitely often on a bounded interval, then the…