4 papers
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…