15 citations · 38 across the 12 of their papers we have counts for
12 papers
On The Spectrum Of Infinite Quantum Graphs
Marco Düfel, James B. Kennedy, Delio Mugnolo +2
We study the interplay between spectrum, geometry and boundary conditions for two distinguished self-adjoint realisations of the Laplacian on infinite metric graphs, the so-called…
On fully supported eigenfunctions of quantum graphs
Marvin Plümer, Matthias Täufer
We prove that every metric graph which is a tree has an orthonormal sequence of Laplace-eigenfunctions of full support. This implies that the number of nodal domains of the $…
Protecting points from operator pencils
Albrecht Seelmann, Matthias Täufer, Krešimir Veselić
We classify all sets of the form where and are self-adjoint operators and is bounded, non-negative, and non-zero. We show…
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…
Eigenfunctions and the Integrated Density of States on Archimedean Tilings
Norbert Peyerimhoff, Matthias Täufer
We study existence and absence of -eigenfunctions of the combinatorial Laplacian on the 11 Archimedean tilings of the Euclidean plane by regular convex polygons. We show th…
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…
Laplace-eigenfunctions on the torus with high vanishing order
Matthias Täufer
We use the sum-of-squares theorem from number theory to construct eigenfunctions of the Laplacian on the -dimensional torus, , which vanish to any prescribed order at…
Unique continuation principles and their absence for Schrödinger eigenfunctions on combinatorial and quantum graphs and in continuum space
Norbert Peyerimhoff, Matthias Täufer, Ivan Veselic
For the analysis of the Schrödinger and related equations it is of central importance whether a unique continuation principle (UCP) holds or not. In continuum Euclidean space quant…
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…
Wegner estimate for Landau-breather Hamiltonians
Matthias Täufer, Ivan Veselic
We consider Landau Hamiltonians with a weak coupling random electric potential of breather type. Under appropriate assumptions we prove a Wegner estimate. It implies the Hoelder co…
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 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…