N. Pattakos

activity

20112025

most citedOn existence of global solutions of the one-dimensional cubic NLS for initial data in the modulation space

M_{p, q} (R)

25 citations · 82 across the 17 of their papers we have counts for

collaborators

17 papers

math-ph2025

On the Excess Charge Problem of Atoms

Dirk Hundertmark, Nikolaos Pattakos, Marvin Raimund Schulz

This paper establishes new bounds on the maximum number of electrons $N_{c} (Z)$ that an atom with nuclear charge $Z$ can bind. Specifically, we show that \begin{equation*} N_c(Z) <…

math.AP2021

Higher order NLS with anisotropic dispersion and modulation spaces: a global existence and scattering result

Leonid Chaichenets, Nikolaos Pattakos

In this paper we transfer a small data global existence and scattering result by Wang and Hudzik to the more general case of modulation spaces $M_{p, q}^{s} (R^{d})$ where $q =…

math.AP2019★ 1 cited

Unconditional uniqueness of higher order nonlinear Schrödinger equations

Friedrich Klaus, Peer Kunstmann, Nikolaos Pattakos

We show the existence of weak solutions in the extended sense of the Cauchy problem for the cubic fourth order nonlinear Schrödinger equation with initial data $u_{0} \in X$ , where…

math.AP2019★ 2 cited

On the global wellposedness of the Klein-Gordon equation for initial data in modulation spaces

Leonid Chaichenets, Nikolaos Pattakos

We prove global wellposedness of the Klein-Gordon equation with power nonlinearity $∣ u ∣^{α - 1} u$ , where $α \in [1, \frac{d}{d - 2}]$ , in dimension $d \geq 3$ with initial data i…

math.AP2019★ 2 cited

On the global well-posedness of the quadratic NLS on $L^{2} (R) + H^{1} (T)$

Leonid Chaichenets, Dirk Hundertmark, Peer Christian Kunstmann +1

We study the one dimensional nonlinear Schrödinger equation with power nonlinearity $∣ u ∣^{α - 1} u$ for $α \in [1, 5]$ and initial data $u_{0} \in L^{2} (R) + H^{1} (T)$ . We…

math.AP2019★ 2 cited

The global Cauchy problem for the NLS with higher order anisotropic dispersion

Leonid Chaichenets, Nikolaos Pattakos

We use a method developed by Strauss to obtain global wellposedness results in the mild sense for the small data Cauchy problem in modulation spaces $M_{p, q}^{s} (R^{d})$ , wher…

math.AP2018★ 4 cited

Knocking out teeth in one-dimensional periodic NLS

Leonid Chaichenets, Dirk Hundertmark, Peer Kunstmann +1

We show the existence of weak solutions in the extended sense of the Cauchy problem for the cubic nonlinear Schrödinger equation in one dimension with initial data $u_{0}$ in $H^{s…

math.AP2018★ 12 cited

Nonlinear Schrödinger equation, differentiation by parts and modulation spaces

Leonid Chaichenets, Dirk Hundertmark, Peer Kunstmann +1

We show the existence of weak solutions in the extended sense of the Cauchy problem for the cubic nonlinear Schrödinger equation in the modulation space $M_{p, q}^{s} (R)$ wh…

math.AP2018★ 8 cited

NLS in the modulation space $M_{2, q} (R)$

Nikolaos Pattakos

We show the existence of weak solutions in the extended sense of the Cauchy problem for the cubic nonlinear Schrödinger equation in the modulation space $M_{2, q}^{s} (R)$ , $…

math.AP2016★ 3 cited

Local well-posedness for the nonlinear Schrödinger equation in the intersection of modulation spaces $M_{p, q}^{s} (R^{d}) \cap M_{\infty, 1} (R^{d})$

Leonid Chaichenets, Dirk Hundertmark, Peer Christian Kunstmann +1

We introduce a Littlewood-Paley characterization of modulation spaces and use it to give an alternative proof of the algebra property, somehow implicitly contained in Sugimoto (201…

math.AP2016★ 25 cited

On existence of global solutions of the one-dimensional cubic NLS for initial data in the modulation space $M_{p, q} (R)$

Leonid Chaichenets, Dirk Hundertmark, Peer Kunstmann +1

We prove global existence for the one-dimensional cubic non-linear Schrödinger equation in modulation spaces $M_{p, p^{'}}$ for $p$ sufficiently close to $2$ . In contrast to known resu…

math.CA2015

A dyadic analysis approach to the problem of continuity of weighted estimates with respect to the $A_{p}$ characteristic

Nikolaos Pattakos

This paper presents a new proof of the results regarding the continuity of weighted estimates with respect to the characteristic of the weight. Here we first prove the result in th…

math.AP2014★ 15 cited

On sharp bilinear Strichartz estimates of Ozawa-Tsutsumi type

Jonathan Bennett, Neal Bez, Chris Jeavons +1

We provide a comprehensive analysis of sharp bilinear estimates of Ozawa-Tsutsumi type for solutions u of the free Schrödinger equation, which give sharp control on $∣ u ∣^{2}$ in clas…

math.CA2013★ 1 cited

Matrix weights, Littlewood Paley inequalities and the Riesz transforms

Nicholas Boros, Nikolaos Pattakos

We discuss weighted estimates for the squares of the Riesz transforms, R^{2}, on L^{2}(W) where W is a matrix A2 weight. We prove that if W is close to the Identity matrix Id, then…

math.CA2012★ 3 cited

Continuity of weighted estimates for sublinear operators

Michael Papadimitrakis, Nikolaos Pattakos

In this note we prove that if a sublinear operator T satisfies a certain weighted estimate in the $L^{p} (w)$ space for all $w \in A_{p}$ , $1 < p < + \infty$ , then the operator norm of T…

math.CA2012

Some remarks on extrapolation with "flat" weights

Nicholas Boros, Nikolaos Pattakos, Alexander Volberg

We prove an extrapolation result for general operators under some weak assumptions on the boundedness of the operator. In particular, we show that if the operator is weakly bounded…

math.CA2011★ 4 cited

The Muckenhoupt $A_{\infty}$ class as a metric space and continuity of weighted estimates

Nikolaos Pattakos, Alexander Volberg

We show how the $A_{\infty}$ class of weights can be considered as a metric space. As far as we know this is the first time that a metric d is considered on this set. We use this met…

On the Excess Charge Problem of Atoms

Higher order NLS with anisotropic dispersion and modulation spaces: a global existence and scattering result

Unconditional uniqueness of higher order nonlinear Schrödinger equations

On the global wellposedness of the Klein-Gordon equation for initial data in modulation spaces

On the global well-posedness of the quadratic NLS on L2(R)+H1(T)

The global Cauchy problem for the NLS with higher order anisotropic dispersion

Knocking out teeth in one-dimensional periodic NLS

Nonlinear Schrödinger equation, differentiation by parts and modulation spaces

NLS in the modulation space M2,q​(R)

Local well-posedness for the nonlinear Schrödinger equation in the intersection of modulation spaces Mp,qs​(Rd)∩M∞,1​(Rd)

On existence of global solutions of the one-dimensional cubic NLS for initial data in the modulation space Mp,q​(R)

A dyadic analysis approach to the problem of continuity of weighted estimates with respect to the Ap​ characteristic

On sharp bilinear Strichartz estimates of Ozawa-Tsutsumi type

Matrix weights, Littlewood Paley inequalities and the Riesz transforms

Continuity of weighted estimates for sublinear operators

Some remarks on extrapolation with "flat" weights

The Muckenhoupt A∞​ class as a metric space and continuity of weighted estimates

On the global well-posedness of the quadratic NLS on $L^{2} (R) + H^{1} (T)$

NLS in the modulation space $M_{2, q} (R)$

Local well-posedness for the nonlinear Schrödinger equation in the intersection of modulation spaces $M_{p, q}^{s} (R^{d}) \cap M_{\infty, 1} (R^{d})$

On existence of global solutions of the one-dimensional cubic NLS for initial data in the modulation space $M_{p, q} (R)$

A dyadic analysis approach to the problem of continuity of weighted estimates with respect to the $A_{p}$ characteristic

The Muckenhoupt $A_{\infty}$ class as a metric space and continuity of weighted estimates