David Damanik

activity

20122025

most citedAlmost Periodicity in Time of Solutions of the KdV Equation

35 citations · 57 across the 5 of their papers we have counts for

collaborators

9 papers

math-ph2025

Ballistic Transport for Discrete Multi-Dimensional Schrödinger Operators With Decaying Potential

David Damanik, Zhiyan Zhao

We consider the discrete Schrödinger operator $H = - Δ + V$ on $ℓ^{2} (Z^{d})$ with a decaying potential, in arbitrary lattice dimension $d \in N^{*}$ , where $Δ$ is the s…

math.SP2020

On Simon's Hausdorff Dimension Conjecture

David Damanik, Jake Fillman, Shuzheng Guo +1

Barry Simon conjectured in 2005 that the Szegő matrices, associated with Verblunsky coefficients ${α_{n}}_{n \in Z_{+}}$ obeying $\sum_{n = 0}^{\infty} n^{γ} ∣ α_{n} ∣^{2} < \infty$ for…

math.AP2015★ 35 cited

Almost Periodicity in Time of Solutions of the KdV Equation

Ilia Binder, David Damanik, Michael Goldstein +1

We study the Cauchy problem for the KdV equation $\partial_{t} u - 6 u \partial_{x} u + \partial_{x}^{3} u = 0$ with almost periodic initial data $u (x, 0) = V (x)$ . We consider initial data $V…

math.SP2015★ 9 cited

Homogeneity of the spectrum for quasi-periodic Schrödinger operators

Michael Goldstein, David Damanik, Wilhelm Schlag +1

We consider the one-dimensional discrete Schrödinger operator $[H (x, ω) φ] (n) \equiv - φ (n - 1) - φ (n + 1) + V (x + nω) φ (n),$ $n \in Z$ , $x, ω \in [0, 1]$ with real-ana…

math.SP2014

A Multi-Scale Analysis Scheme on Abelian Groups with an Application to Operators Dual to Hill's Equation

David Damanik, Michael Goldstein, Milivoje Lukic

We present an abstract multiscale analysis scheme for matrix functions $(H_{ε} (m, n))_{m, n \in T}$ , where $T$ is an Abelian group equipped with a dist…

math.SP2014★ 13 cited

The Isospectral Torus of Quasi-Periodic Schrödinger Operators via Periodic Approximations

David Damanik, Michael Goldstein, Milivoje Lukic

We study the quasi-periodic Schrödinger operator $- ψ " (x) + V (x) ψ (x) = E ψ (x), x \in R$ in the regime of "small" $V(x) = \sum_{m\in\mathbb{Z}^ν}c(m)\exp (2πi mω…

math.SP2014

The Spectrum of a Schrödinger Operator With Small Quasi-Periodic Potential is Homogeneous

David Damanik, Michael Goldstein, Milivoje Lukic

We consider the quasi-periodic Schrödinger operator $[H ψ] (x) = - ψ " (x) + V (x) ψ (x)$ in $L^{2} (R)$ , where the potential is given by $$ V(x) = \sum_{m \in \mathbb{Z}^ν\set…

math.AP2012

On the Existence and Uniqueness of Global Solutions for the KdV Equation with Quasi-Periodic Initial Data

David Damanik, Michael Goldstein

We consider the KdV equation $\partial_{t} u + \partial_{x}^{3} u + u \partial_{x} u = 0$ with quasi-periodic initial data whose Fourier coefficients decay exponentially and prove existence…

math.SP2012

On the Inverse Spectral Problem for the Quasi-Periodic Schrödinger Equation

David Damanik, Michael Goldstein

We study the quasi-periodic Schrödinger equation $$ -ψ"(x) + V(x) ψ(x) = E ψ(x), \qquad x \in \IR $$ in the regime of "small" $V$ . Let $(E_{m}^{'}, E "_{m})$ , $m \in \zv$, be the standard l…