Related papers: On the stability of the differential process gener…

We derive two estimates for the deviation of the $N$-particle, hard-spheres Kac process from the corresponding Boltzmann equation, measured in expected Wasserstein distance. Particular care is paid to the long-time properties of our…

We study couples of interpolators, the differentials they generate and their associated commutator theorems. An essential part of our analysis is the study of the intrinsic symmetries of the process. Since we work without any compatibility…

We show that bounded cohomology stabilizes along sequences of classical Lie groups, and along sequences of lattices in them. Our method is based on a criterion from (arXiv:2307.12808) which adapts Quillen's stability method to the setting…

We prove an optimal result of stability under $\ell_p$-sums of some concentration properties for Lipschitz maps defined on Hamming graphs into Banach spaces. As an application, we give examples of spaces with Szlenk index arbitrarily high…

Real smooth three-dimensional or higher Banach spaces are isomorphic with respect to the nonlinear structure of Birkhoff-James orthogonality if and only if they are isometrically isomorphic. Moreover, using smooth Radon planes and…

We study the inverse boundary value problems of determining a potential in the Helmholtz type equation for the perturbed biharmonic operator from the knowledge of the partial Cauchy data set. Our geometric setting is that of a domain whose…

We study the group invariant continuous polynomials on a Banach space $X$ that separate a given set $K$ in $X$ and a point $z$ outside $K$. We show that if $X$ is a real Banach space, $G$ is a compact group of $\mathcal{L} (X)$, $K$ is a…

We prove various results involving arcs - which generalise test configurations - within the theory of K-stability. Our main result characterises coercivity of the Mabuchi functional on spaces of Fubini-Study metrics in terms of uniform…

We study the lattice structure of the family of weakly compact subsets of the unit ball $B_X$ of a separable Banach space $X$, equipped with the inclusion relation (this structure is denoted by $\mathcal{K}(B_X)$) and also with the…

Motivated by the operad built from moduli spaces of Riemann surfaces, we consider a general class of operads in the category of spaces that satisfy certain homological stability conditions. We prove that such operads are infinite loop space…

We prove that an interpolation pair of Banach lattices is uniquely determined by the collection of intermediate spaces with the property that these are interpolation spaces for positive operators. A correspondent result for exact…

In this work characterizations of notions of output stability for uncertain time-varying systems described by retarded functional differential equations are provided. Particularly, characterizations by means of Lyapunov and Razumikhin…

While it is well known that nonlinear methods of approximation can often perform dramatically better than linear methods, there are still questions on how to measure the optimal performance possible for such methods. This paper studies…

The main aim of this paper is to develop a general approach, which allows to extend the basics of Brudnyi-Kruglyak interpolation theory to the realm of quasi-Banach lattices. We prove that all $K$-monotone quasi-Banach lattices with respect…

For linear random dynamical systems in a separable Banach space $X$, we derived a series of Krein-Rutman type Theorems with respect to co-invariant cone family with rank-$k$, which present a (quasi)-equivalence relation between the…

It is well-known that in Banach spaces with finite cotype, the $R$-bounded and $\gamma$-bounded families of operators coincide. If in addition $X$ is a Banach lattice, then these notions can be expressed as square function estimates. It is…

Multiplicative and additive $D$-stability, diagonal stability, Schur $D$-stability, $H$-stability are classical concepts which arise in studying linear dynamical systems. We unify these types of stability, as well as many others, in one…

This paper is concerned with the differential sensitivity analysis of variational inequalities in Banach spaces whose solution operators satisfy a generalized Lipschitz condition. We prove a sufficient criterion for the directional…

In this paper, we prove that the existence of an $\varepsilon$-isometry from a separable Banach space $X$ into $Y$ (the James space or a reflexive space) implies the existence of a linear isometry from $X$ into $Y$. Then we present a set…

In this paper, we shall show that a polarized algebraic manifold is K-stable if the polarization class admits a Kaehler metric of constant scalar curvature. This generalizes the results of Chen-Tian, Donaldson and Stoppa. (Parts of the…