25 citations · 84 across the 16 of their papers we have counts for
18 papers
A Hörmander spectral multiplier theorem for fractional Hardy operators
Konstantin Merz
We consider the fractional Laplacian with added critical or subcritical Hardy potential, called Hardy operator. We prove a Hörmander spectral multiplier theorem, i.e., the boundedn…
On wave operators for Hardy operators with and without perturbations
Atsuhide Ishida, Konstantin Merz
We prove asymptotic completeness of the wave operators in time-dependent scattering theory which intertwine the ordinary or fractional Laplacian and the corresponding Hardy operato…
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…
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…
Subordinated Bessel heat kernels
Krzysztof Bogdan, Konstantin Merz
We prove new bounds for Bessel heat kernels and Bessel heat kernels subordinated by stable subordinators. In particular, we provide a 3G inequality in the subordinated case.
Ground state representation for the fractional Laplacian with Hardy potential in angular momentum channels
Krzysztof Bogdan, Konstantin Merz
Motivated by the study of relativistic atoms, we consider the Hardy operator acting on functions of the form in $L^2(\m…
On Sobolev norms involving Hardy operators in a half-space
Rupert L. Frank, Konstantin Merz
We consider Hardy operators on the half-space, that is, ordinary and fractional Schrödinger operators with potentials given by the appropriate power of the distance to the boundary…
The Scott conjecture for large Coulomb systems: a review
Rupert L. Frank, Konstantin Merz, Heinz Siedentop
We review some older and more recent results concerning the energy and particle distribution in ground states of heavy Coulomb systems. The reviewed results are asymptotic in natur…
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…
On complex-time heat kernels of fractional Schrödinger operators via Phragmén-Lindelöf principle
Konstantin Merz
We consider fractional Schrödinger operators with possibly singular potentials and derive certain spatially averaged estimates for its complex-time heat kernel. The main tool is a…
Relativistic Strong Scott Conjecture: A Short Proof
Rupert L. Frank, Konstantin Merz, Heinz Siedentop
We consider heavy neutral atoms of atomic number modeled with kinetic energy used already by Chandrasekhar. We study the behavior of the one-particle g…
Proof of the Strong Scott Conjecture for Heavy Atoms: the Furry Picture
Konstantin Merz, Heinz Siedentop
We prove the convergence of the density on the scale to the density of the Bohr atom (with infinitely many electrons) (strong Scott conjecture) for a model that is known t…
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…
Proof of the Strong Scott Conjecture for Chandrasekhar Atoms
Rupert L. Frank, Konstantin Merz, Heinz Siedentop +1
We consider a large neutral atom of atomic number , taking relativistic effects into account by assuming the dispersion relation . We study the behavior of th…
On Scales of Sobolev spaces associated to generalized Hardy operators
Konstantin Merz
We consider the fractional Laplacian with Hardy potential and study the scale of homogeneous Sobolev spaces generated by this operator. Besides generalized and reversed Hardy…
The Atomic Density on the Thomas--Fermi Length Scale for the Chandrasekhar Hamiltonian
Konstantin Merz, Heinz Siedentop
We consider a large neutral atom of atomic number , modeled by a pseudo-relativistic Hamiltonian of Chandrasekhar. We study its suitably rescaled one-particle ground state densi…
Equivalence of Sobolev norms involving generalized Hardy operators
Rupert L. Frank, Konstantin Merz, Heinz Siedentop
We consider the fractional Schrödinger operator with Hardy potential and critical or subcritical coupling constant. This operator generates a natural scale of homogeneous Sobolev s…