The present research monograph is a testimony to the fact that Fractal Analysis is deeply
connected to numerous areas of contemporary Mathematics. Here, we have in mind, in …

For artificial deep neural networks, we prove expression rates for analytic functions in the
norm of where. Here denotes the Gaussian product probability measure on. We consider in …

For Bayesian inverse problems with input-to-response maps given by well-posed partial
differential equations and subject to uncertain parametric or function space input, we …

For two probability measures ρ and π on [-1, 1] N we investigate the approximation of the
triangular Knothe–Rosenblatt transport T:[-1, 1] N→[-1, 1] N that pushes forward ρ to π …

We prove that the free energy of the log-gamma polymer between lattice points (1, 1) and
(M, N) converges to the GUE Tracy–Widom distribution in the M 1/3 scaling, provided that …

We deduce a product formula for the Whittaker function W κ, μ whose kernel does not
depend on the second parameter. Making use of this formula, we define the positivity …

Using a sum rule, we derive new bounds on Herglotz functions that generalize those given
in Bernland et al.[J. Phys. A: Math. Theor. 44 (14), 145205 (2011)] and Gustafsson and …

Lévy processes with respect to the Whittaker convolution Page 1 TRANSACTIONS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 374, Number 4, April 2021, Pages 2383–2419 …

Fractal tube Formulas for compact sets and relative fractal drums Page 1 J. Fractal Geom. 5 (2018),
1–119 DOI 10.4171/JFG/57 Journal of Fractal Geometry © European Mathematical Society …

We study the moments of the distance traveled by a walk in the plane with unit steps in
random directions. While this historically interesting random walk is well understood from a …