4 citations · 6 across the 13 of their papers we have counts for
14 papers
Spectral Barron spaces of periodic functions
Mourad Choulli, Shuai Lu, Hiroshi Takase
Spectral Barron spaces are Fourier-Lebesgue-type spaces that arise in the approximation of functions by neural networks. Conventional spectral Barron spaces are mostly considered o…
Heat equations in spectral Barron spaces
Mourad Choulli, Shuai Lu, Hiroshi Takase
Spectral Barron spaces, characterized by an \(L^1\)-based Fourier-Lebesgue norm, have earned significant attention in approximation theory due to their remarkable capacity to repre…
Determination of separable perturbations of an unbounded potential in the two-dimensional Schrödinger equation
Mourad Choulli, Hiroshi Takase
We establish uniqueness and stability results for a class of perturbations of an unbounded potential in the two-dimensional Schrödinger equation, from the corresponding Dirichlet-t…
An - Carleman inequality for
Mourad Choulli, Hiroshi Takase
In this note, by refining the proof of the Carleman inequality obtained by Dos Santos, Kenig, and Salo in 2013, we establish a new - Carleman inequality.
Quantitative Borg-Levinson theorem for the magnetic Schödinger operator with unbounded electrical potential
Mourad Choulli, Hiroshi Takase
The first author established in [8] a quantitative Borg-Levinson theorem for the Schrödinger operator with unbounded potential. In the present work, we extend the results in [8] to…
Functional analysis and partial differential equations in spectral Barron spaces
Mourad Choulli, Shuai Lu, Hiroshi Takase
Spectral Barron spaces, constituting a specialized class of function spaces that serve as an interdisciplinary bridge between mathematical analysis, partial differential equations…
Quantitative uniqueness of continuation for the Schrödinger equation : explicit dependence on the potential
Mourad Choulli, Hiroshi Takase
We demonstrate a quantitative version of the usual properties related to unique continuation from an interior datum for the Schrödinger equation with bounded or unbounded potential…
Stability for an inverse flux and an inverse boundary coefficient problems
Mourad Choulli, Shuai Lu, Hiroshi Takase
We establish both Lipschitz and logarithmic stability estimates for an inverse flux problem and subsequently apply these results to an inverse boundary coefficient problem. Further…
Stable determination of the potential for the Helmholtz equation in the high frequency limit from boundary measurements
Mourad Choulli, Hiroshi Takase
We establish a triple logarithmic stability estimate of determining the potential in a Helmholtz equation from a partial Dirichlet-to-Neumann map in the high frequency limit. This…
An inverse obstacle problem for the magnetic Schrödinger equation
Mourad Choulli, Hiroshi Takase
We establish stability inequalities of an inverse obstacle problem for the magnetic Schrödinger equation. We mainly study the problem of reconstructing an unknown function defined…
New quantitative unique continuation result for elliptic equations
Mourad Choulli, Hiroshi Takase
We prove a new quantitative unique continuation result for elliptic equations from Cauchy data. We provide a simple and direct proof based only on a Carleman inequality. Similar re…
An inverse hyperbolic obstacle problem
Mourad Choulli, Hiroshi Takase
We establish Hölder stability of an inverse hyperbolic obstacle problem. Mainly, we study the problem of reconstructing an unknown function defined on the boundary of the obstacle…
Lipschitz stability for an elliptic inverse problem with two measurements
Mourad Choulli, Hiroshi Takase
We consider the problem of determining the unknown boundary values of a solution of an elliptic equation outside a bounded open set from the knowledge of the values of this sol…
A Carleman estimate and an energy method for a first-order symmetric hyperbolic system
G. Floridia, H. Takase, M. Yamamoto
For a symmetric hyperbolic system of the first order, we prove a Carleman estimate under some positivity condition concerning the coefficient matrices. Next, applying the Carleman…