12 citations · 38 across the 16 of their papers we have counts for
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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…
Anchored heat kernel upper bounds on graphs with unbounded geometry and anti-trees
Matthias Keller, Christian Rose
We derive Gaussian heat kernel bounds on graphs with respect to a fixed origin for large times under the assumption of a Sobolev inequality and volume doubling on large balls. The…
Gaussian upper bounds for heat kernels on graphs with unbounded geometry
Matthias Keller, Christian Rose
We prove large-time Gaussian upper bounds for continuous-time heat kernels of Laplacians on graphs with unbounded geometry. Our estimates hold for centers of large balls satisfying…
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…
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…
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…