63 citations · 837 across the 76 of their papers we have counts for
76 papers
Quantitative concentration inequalities for the uniform approximation of the IDS
Max Kämper, Christoph Schumacher, Fabian Schwarzenberger +1
The integrated density of states (IDS) is a fundamental spectral quantity for quantum Hamiltonians modeling condensed matter systems, describing how densely energy levels are distr…
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…
Spherical Logvinenko-Sereda-Kovrijkine type inequality and null-controllability of the heat equation on the sphere
Alexander Dicke, Ivan Veselic
It is shown that the restriction of a polynomial to a sphere satisfies a Logvinenko-Sereda-Kovrijkine type inequality (a specific type of uncertainty relation). This implies a spec…
Spectral inequality with sensor sets of decaying density for Schrödinger operators with power growth potentials
Alexander Dicke, Albrecht Seelmann, Ivan Veselic
We prove a spectral inequality (a specific type of uncertainty relation) for Schrödinger operators with confinement potentials, in particular of Shubin-type. The sensor sets are al…
Uncertainty principle for Hermite functions and null-controllability with sensor sets of decaying density
Alexander Dicke, Albrecht Seelmann, Ivan Veselic
We establish a family of uncertainty principles for finite linear combinations of Hermite functions. More precisely, we give a geometric criterion on a subset $S\subset \RR^d$ ensu…
Control problem for quadratic parabolic differential equations with sparse sensor sets of finite volume or anisotropically decaying density
Alexander Dicke, Albrecht Seelmann, Ivan Veselic
We prove observability and null-controllability for quadratic parabolic differential equations. The sensor set is allowed to be sparse and have finite volume if the generator has t…