39 citations · 127 across the 28 of their papers we have counts for
33 papers
Space curve Fourier restriction for orthonormal functions
Jean-Claude Cuenin, Jacob Denson, Jonathan Hickman
We prove a variant of the Fourier restriction inequality for non-degenerate curves in the setting of orthonormal systems. To achieve this, we develop a Hilbert space approach…
Random Schrödinger operators on manifolds and abstract bounds for multiplier-type operators
Jean-Claude Cuenin, Konstantin Merz, Eduard Stefanescu
We study random Schrödinger operators on closed Riemannian manifolds with Anderson-type potentials. We prove high-probability spectral inclusion bounds showing that eigenvalues rem…
Orthonormal Spectral Cluster Bounds on Manifolds with Nonpositive Curvature
Jean-Claude Cuenin, Ngoc Nhi Nguyen, Xiaoyan Su
Let be a closed -dimensional Riemannian manifold with nonpositive sectional curvature. We prove sharp, logarithmically improved spectral cluster bounds for orthonormal s…
Smoothing inequalities for transport metrics in compact spaces
Bence Borda, Jean-Claude Cuenin
We prove general upper estimates for the distance between two Borel probability measures in Wasserstein metric in terms of the Fourier transforms of the measures. We work in compac…
Spectral cluster bounds for orthonormal functions on manifolds with nonsmooth metrics
Jean-Claude Cuenin, Ngoc Nhi Nguyen, Xiaoyan Su
We establish spectral cluster bounds for families of orthonormal functions associated to the Laplace-Beltrami operator on a compact Riemannian manifold. The metric is only as…
Eigenvalue bounds for Schrödinger operators with complex potentials on compact manifolds
Jean-Claude Cuenin
We prove eigenvalue bounds for Schrödinger operator on compact manifolds with complex potentials . The bounds depend only on an -norm of the potential, and they ar…
Open problem: Violation of locality for Schrödinger operators with complex potentials
Jean-Claude Cuenin, Rupert L. Frank
We explain in which sense Schrödinger operators with complex potentials appear to violate locality (or Weyl's asymptotics), and we pose three open problems related to this phenomen…
Bounds for Eigenvalue Sums of Schrödinger Operators with Complex Radial Potentials
Jean-Claude Cuenin, Solomon Keedle-Isack
We consider eigenvalue sums of Schrödinger operators on with complex radial potentials , . We prove quantitative bounds on the distribution…
Resolvent estimates in Schatten spaces for Laplace-Beltrami operators on compact manifolds
Jean-Claude Cuenin
We prove resolvent estimates in Schatten spaces for Laplace-Beltrami operators on compact manifolds at the critical exponent. Our proof only uses known bounds for the Hadamard para…
Lieb-Thirring-type inequalities for random Schrödinger operators with complex potentials
Jean-Claude Cuenin, Konstantin Merz
We review some results and proofs on eigenvalue bounds for random Schrödinger operators with complex-valued potentials. We also include new Schatten norm estimates for the resolven…
Effective upper bounds on the number of resonance in potential scattering
Jean-Claude Cuenin
We prove upper bounds on the number of resonances and eigenvalues of Schrödinger operators with complex-valued potentials, where is odd. The novel feature of our u…
On the number and sums of eigenvalues of Schrödinger-type operators with degenerate kinetic energy
Jean-Claude Cuenin, Konstantin Merz
We estimate sums of functions of negative eigenvalues of Schrödinger-type operators whose kinetic energy vanishes on a codimension one submanifold. Our main technical tool is the S…
Random Schrödinger operators with complex decaying potentials
Jean-Claude Cuenin, Konstantin Merz
We prove that the eigenvalues of a continuum random Schrödinger operator of Anderson type, with complex decaying potential, can be bounded (with high probability) in term…
Counterexample to the Laptev--Safronov conjecture
Sabine Bögli, Jean-Claude Cuenin
We prove that the Laptev--Safronov conjecture (Comm. Math. Phys., 2009) is false in the range that is not covered by Frank's positive result (Bull. Lond. Math. Soc., 2011). The sim…
Fourier transform of surface--carried measures of two-dimensional generic surfaces and applications
Jean-Claude Cuenin, Robert Schippa
We give a simple proof of the sharp decay of the Fourier-transform of surface-carried measures of two-dimensional generic surfaces. The estimates are applied to prove Strichartz an…
Schrödinger operators with complex sparse potentials
Jean-Claude Cuenin
We establish quantitative upper and lower bounds for Schrödinger operators with complex potentials that satisfy some weak form of sparsity. Our first result is a quantitative versi…
Sharp time decay estimates for the discrete Klein-Gordon equation
Jean-Claude Cuenin, Isroil A. Ikromov
We establish sharp time decay estimates for the the Klein-Gordon equation on the cubic lattice in dimensions . The dispersive decay rate is $|t|^{…
From spectral cluster to uniform resolvent estimates on compact manifolds
Jean-Claude Cuenin
It is well known that uniform resolvent estimates imply spectral cluster estimates. We show that the converse is also true in some cases. In particular, the universal spectral clus…
Weak coupling limit for Schrödinger-type operators with degenerate kinetic energy for a large class of potentials
Jean-Claude Cuenin, Konstantin Merz
We improve results by Frank, Hainzl, Naboko, and Seiringer [12] and Hainzl and Seiringer [20] on the weak coupling limit of eigenvalues for Schrödinger-type operators whose kinetic…
Sharp spectral bounds for complex perturbations of the indefinite Laplacian
Jean-Claude Cuenin, Orif O. Ibrogimov
We derive quantitative bounds for eigenvalues of complex perturbations of the indefinite Laplacian on the real line. Our results substantially improve existing results even for rea…
Lieb-Thirring inequalities for an effective Hamiltonian of bilayer graphene
Philippe Briet, Jean-Claude Cuenin, Leonid Golinskii +1
Combining the methods of Cuenin [2019] and Borichev-Golinskii-Kupin [2009, 2018], we obtain the so-called Lieb-Thirring inequalities for non-selfadjoint perturbations of an effecti…
Improved eigenvalue bounds for Schrödinger operators with slowly decaying potentials
Jean-Claude Cuenin
We extend a result of Davies and Nath on the location of eigenvalues of Schrödinger operators with slowly decaying complex-valued potentials to higher dimensions. In this context,…
Eigenvalue estimates for bilayer graphene
Jean-Claude Cuenin
Recently, Ferrulli-Laptev-Safronov (2016arXiv161205304F) obtained eigenvalue estimates for an operator associated to bilayer graphene in terms of norms of the (possibly non-s…
Embedded eigenvalues of generalized Schrödinger operators
Jean-Claude Cuenin
We provide examples of operators with decaying potentials that have embedded eigenvalues. The decay of the potential depends on the curvature of the Fermi surfaces of cons…