38 citations · 237 across the 33 of their papers we have counts for
15 papers · 1 filter
Sampling and equidistribution theorems for elliptic second order operators, lifting of eigenvalues, and applications
Martin Tautenhahn, Ivan Veselic
We consider elliptic second order partial differential operators with Lipschitz continuous leading order coefficients on finite cubes and the whole Euclidean space. We prove quanti…
Unique continuation estimates on manifolds with Ricci curvature bounded below
Christian Rose, Martin Tautenhahn
We prove quantitative unique continuation estimates for relatively dense sets and spectral subspaces associated to small energies of Schrödinger operators on Riemannian manifolds w…
Quantitative unique continuation for spectral subspaces of Schrödinger operators with singular potentials
Alexander Dicke, Christian Rose, Albrecht Seelmann +1
Recent (scale-free) quantitative unique continuation estimates for spectral subspaces of Schrödinger operators are extended to allow singular potentials such as certain -funct…
Null-controllability and control cost estimates for the heat equation on unbounded and large bounded domains
Michela Egidi, Ivica Nakić, Albrecht Seelmann +3
We survey recent results on the control problem for the heat equation on unbounded and large bounded domains. First we formulate new uncertainty relations, respectively spectral in…
Sharp estimates and homogenization of the control cost of the heat equation on large domains
Ivica Nakić, Matthias Täufer, Martin Tautenhahn +1
We prove new bounds on the control cost for the abstract heat equation, assuming a spectral inequality or uncertainty relation for spectral projectors. In particular, we specify qu…
Scale-free unique continuation principle, eigenvalue lifting and Wegner estimates for random Schrödinger operators
Ivica Nakić, Matthias Täufer, Martin Tautenhahn +1
We prove a scale-free, quantitative unique continuation principle for functions in the range of the spectral projector of a Schrödinger operator on a c…
Scale-free and quantitative unique continuation for infinite dimensional spectral subspaces of Schrödinger operators
Matthias Täufer, Martin Tautenhahn
We prove a quantitative unique continuation principle for infinite dimensional spectral subspaces of Schrödinger operators. Let and be a Sch…
Harmonic Analysis and Random Schrödinger Operators
Matthias Täufer, Martin Tautenhahn, Ivan Veselic
This survey is based on a series of lectures given during the \emph{School on Random Schrödinger Operators} and the \emph{International Conference on Spectral Theory and Mathematic…
Scale-free quantitative unique continuation and equidistribution estimates for solutions of elliptic differential equations
Denis Borisov, Martin Tautenhahn, Ivan Veselic
We consider elliptic differential operators on either the entire Euclidean space or on subsets consisting of a cube of integer length . For eigenfunctions o…
Sampling inequality for -norms of eigenfunctions, spectral projectors, and Weyl sequences of Schrödinger operators
Martin Tautenhahn, Ivan Veselić
We consider a Schrödinger operator with bounded, measurable potential in multidimensional Euclidean space. We prove for every -eigenfunction a quantitative equidistribution es…
A quantitative Carleman estimate for second order elliptic operators
Ivica Nakić, Christian Rose, Martin Tautenhahn
We prove a Carleman estimate for elliptic second order partial differential operators with Lipschitz continuous coefficients. The Carleman estimate is valid for any complex-valued…
Scale-free uncertainty principles and Wegner estimates for random breather potentials
Ivica Nakić, Matthias Täufer, Martin Tautenhahn +1
We present new scale-free quantitative unique continuation principles for Schrödinger operators. They apply to linear combinations of eigenfunctions corresponding to eigenvalues be…
Multiscale unique continuation properties of eigenfunctions
Denis Borisov, Ivica Nakić, Christian Rose +2
Quantitative unique continuation principles for multiscale structures are an important ingredient in a number applications, e.g. random Schrödinger operators and control theory. We…
Equidistribution estimates for eigenfunctions and eigenvalue bounds for random operators
Denis Borisov, Martin Tautenhahn, Ivan Veselic
We discuss properties of -eigenfunctions of Schrödinger operators and elliptic partial differential operators. The focus is set on unique continuation principles and equidistr…
Wegner estimate and localization for alloy-type models with sign-changing exponentially decaying single-site potentials
Karsten Leonhardt, Norbert Peyerimhoff, Martin Tautenhahn +1
We study Schrödinger operators on $L^2 (\RR^d)$ and $\ell^2(\ZZ^d)$ with a random potential of alloy-type. The single-site potential is assumed to be exponentially decaying but not…