38 citations · 237 across the 33 of their papers we have counts for
34 papers
Uncertainty principles and lower bounds for Schrödinger operators
Albrecht Böttcher, Peter Stollmann, Martin Tautenhahn
We prove that two different abstract quantitative uncertainty principles are equivalent to the strict positivity of the associated abstract Schrö\-din\-ger operators. We also discu…
On controllability, observability and stabilizability of the heat equation on discrete graphs
Florentin Münch, Christian Seifert, Peter Stollmann +1
We consider linear control problems for the heat equation of the form , , where is the weighted Laplacian on…
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…
A Logvinenko-Sereda theorem for vector-valued functions and application to control theory
Clemens Bombach, Martin Tautenhahn
We prove a Logvinenko-Sereda Theorem for vector valued functions. That is, for an arbitrary Banach space , all , all , all $f \in L^p (\math…
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…
Observability for Non-autonomous Systems
Clemens Bombach, Fabian Gabel, Christian Seifert +1
We study non-autonomous observation systems \begin{align*} \dot{x}(t) = A(t) x(t),\quad y(t) = C(t) x(t),\quad x(0) = x_0\in X, \end{align*} where is a strongly measurable…
Optimal control of parabolic equations -- a spectral calculus based approach
Luka Grubišić, Martin Lazar, Ivica Nakić +1
In this paper we consider a constrained parabolic optimal control problem. The cost functional is quadratic and it combines the distance of the trajectory of the system from the de…
Sufficient criteria for stabilization properties in Banach spaces
Michela Egidi, Dennis Gallaun, Christian Seifert +1
We study abstract sufficient criteria for open-loop stabilizability of linear control systems in a Banach space with a bounded control operator, which build up and generalize a suf…
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…
Observability and null-controllability for parabolic equations in -spaces
Clemens Bombach, Dennis Gallaun, Christian Seifert +1
We study (approximate) null-controllability of parabolic equations in and provide explicit bounds on the control cost. In particular we consider systems of the…
Sufficient criteria and sharp geometric conditions for observability in Banach spaces
Dennis Gallaun, Christian Seifert, Martin Tautenhahn
Let be Banach spaces, a -semigroup on , the corresponding infinitesimal generator on , a bounded linear operator from to , and $…
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…
Unique continuation and lifting of spectral band edges of Schrödinger operators on unbounded domains (With an Appendix by Albrecht Seelmann)
Ivica Nakić, Matthias Täufer, Martin Tautenhahn +2
We prove and apply two theorems: First, a quantitative, scale-free unique continuation estimate for functions in a spectral subspace of a Schrödinger operator on a bounded or unbou…
Wegner estimate for discrete Schrödinger operators with Gaussian random potentials
Martin Tautenhahn
We prove a Wegner estimate for discrete Schrödinger operators with a potential given by a Gaussian random process. The only assumption is that the covariance function decays expone…
Wegner estimate and disorder dependence for alloy-type Hamiltonians with bounded magnetic potential
Matthias Täufer, Martin Tautenhahn
We consider non-ergodic magnetic random Schödinger operators with a bounded magnetic vector potential. We prove an optimal Wegner estimate valid at all energies. The proof is an ad…
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…