We survey the adversarial robustness of neural networks from the perspective of Lipschitz
calculus in a unifying fashion by expressing models, attacks and safety guarantees, that is, a …

The analysis of eigenvalues of Laplace and Schrödinger operators is an important and
classical topic in mathematical physics with many applications. This book presents a …

Our main goal in this long survey article is to provide an overview of the theory of complex
fractal dimensions and of the associated geometric or fractal zeta functions, first in the case …

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 …

Fractional Sobolev extension and imbedding Page 1 TRANSACTIONS OF THE AMERICAN
MATHEMATICAL SOCIETY Volume 367, Number 2, February 2015, Pages 959–979 S 0002-9947(2014)06088-1 …

In the setting of metric measure spaces equipped with a doubling measure supporting a
weak p-Poincaré inequality with 1⩽ p<∞, we show that any uniform domain Ω is an …

We show that, under general conditions, the operator (-∇. μ ∇+ 1)^ 1/2 (-∇. μ∇+ 1) 1/2 with
mixed boundary conditions provides a topological isomorphism between W^ 1, p _D (Ω)\rm …

This thesis explores the $ L^ 2$-Theory for nonlocal operators of L\'evy type on bounded
domains, as well as their local counterparts. The research was completed at Bielefeld …

Our aim in this paper is to show that the Riesz potential operator I α (⋅) of variable order α
(⋅) embeds from variable exponent Morrey spaces L p (⋅), ν (⋅)(G) to Campanato–Morrey …

We show that a domain is an extension domain for a Hajłasz–Besov or for a Hajłasz–Triebel–
Lizorkin space if and only if it satisfies a measure density condition. We use a modification of …