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math.AP2017
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…
math-ph2017★ 2 cited
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…