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math.AP2019★ 147 cited
Time fractional diffusion equations: solution concepts, regularity and long-time behaviour
Rico Zacher
In this paper we give a survey of results on various analytical aspects of time fractional diffusion equations. We describe the approach via abstract Volterra equations and collect…
math.AP2019
The Fractional Laplacian has Infinite Dimension
Adrian Spener, Frederic Weber, Rico Zacher
We show that the fractional Laplacian on fails to satisfy the Bakry-Émery curvature-dimension inequality for all curvature bounds and all…
math.AP2019
Curvature-dimension inequalities for non-local operators in the discrete setting
Adrian Spener, Frederic Weber, Rico Zacher
We study Bakry-Émery curvature-dimension inequalities for non-local operators on the one-dimensional lattice and prove that operators with finite second moment have finite dimensio…