Related papers: Dilatation structures with the Radon-Nikodym prope…
By a classical principle of probability theory, sufficiently thin subsequences of general sequences of random variables behave like i.i.d.\ sequences. This observation not only explains the remarkable properties of lacunary trigonometric…
In this paper we define the Radon-Nikodym class (RN class) of locally convex topological vector spaces. The RN class is characterized in terms of the Radon-Nikodym theorem for vector measures using integrable by seminorm derivatives. It is…
We study when diameter two properties pass down to subspaces. We obtain that the slice two property (respectively diameter two property, strong diameter two property) passes down from a Banach space $X$ to a subspace $Y$ whenever $Y$ is…
This is a pedagogical introduction covering maps of metric spaces, Gromov-Hausdorff distance and its "physical" meaning, and dilation structures as a convenient simplification of an exhaustive database of maps of a metric space into…
In this paper, we introduce a notion of geometric Banach property (T) for metric spaces, which jointly generalizes Banach property (T) for groups and geometric property (T) for metric spaces. Our framework is achieved by Banach…
We prove that every isometry between the unit spheres of 2-dimensional Banach spaces extends to a linear isometry of the Banach spaces. This resolves the famous Tingley's problem in the class of 2-dimensional Banach spaces.
In this paper, we offer a new perspective on persistent homology by integrating key concepts from metric geometry. For a given compact subset $\mathcal{X}$ of a Banach space $\mathbf{Y}$, we analyze the topological features arising in the…
We describe how generalized complex geometry, which interpolates between complex and symplectic geometry, is compatible with T-duality, a relation between quantum field theories discovered by physicists. T-duality relates topologically…
Araci et al. introduced a $p$-adic $(\rho,q)$-analogue of the Haar distribution. By means of the distribution, they constructed the $p$-adic $(\rho,q)$-Volkenborn integral. In this paper, by virtue of the Mahler expansion of continuous…
In a previous paper [FT1], for any logarithmic symplectic pair (X,D) of a symplectic manifold X and a simple normal crossings symplectic divisor D, we introduced the notion of log pseudo-holomorphic curve and proved a compactness theorem…
We develop a variational framework to understand the properties of the functions learned by neural networks fit to data. We propose and study a family of continuous-domain linear inverse problems with total variation-like regularization in…
Duality cascades are a series of duality transformations in field theories, which can be realized as the Hanany-Witten transitions in brane configurations on a circle. In the setup of the ABJM theory and its generalizations, from the…
We study the approximate differentiability of measurable mappings of Carnot--Carath\'eodory spaces. We show that the approximate differentiability almost everywhere is equivalent to the approximate differentiability along the basic…
We prove that if a complete connected $n$-dimensional Riemannian manifold $M$ has radial sectional curvature at a base point $p\in M$ bounded from below by the radial curvature function of a two-sphere of revolution $\widetilde M$ belonging…
By generalising Rudin's construction of an aperiodic sequence, we derive new substitution-based structures which have purely absolutely continuous diffraction and mixed dynamical spectrum, with absolutely continuous and pure point parts. We…
We generalize the notion of metallic structure in the pseudo-Riemannian setting, define the metallic Norden structure and study its integrability. We consider metallic maps between metallic manifolds and give conditions under which they are…
In 1992, Kiendi, Adamy and Stelzner investigated under which conditions a certain type of function constituted a Lyapunov function for some time-invariant linear system. Six years later, it was obtained that this property holds if and only…
This article provides an overview of various notions of shape spaces, including the space of parametrized and unparametrized curves, the space of immersions, the diffeomorphism group and the space of Riemannian metrics. We discuss the…
Motivated by a general dilation theory for operator-valued measures, framings and bounded linear maps on operator algebras, we consider the dilation theory of the above objects with special structures. We show that every operator-valued…
We prove the existence of measurable invariant manifolds for small perturbations of linear Random Dynamical Systems evolving on a Banach space and admitting a general type of dichotomy, both for continuous and discrete time. Moreover, the…