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In this work infinitely divisible cylindrical probability measures on arbitrary Banach spaces are introduced. The class of infinitely divisible cylindrical probability measures is described in terms of their characteristics, a…
The main purpose of the paper is to present some recent results on metric characterizations of superreflexivity and the Radon-Nikod\'ym property.
This paper addresses the study and characterizations of variational convexity of extended-real-valued functions on Banach spaces. This notion has been recently introduced by Rockafellar, and its importance has been already realized and…
We extend some recent results on the Hausdorff convergence of level-sets for total variation regularized linear inverse problems. Dimensions higher than two and measurements in Banach spaces are considered. We investigate the relation…
The present document is the draft of a book which presents an introduction to infinite-dimensional differential geometry beyond Banach manifolds. As is well known the usual calculus breaks down in this setting. Hence, we replace it by the…
Let $ H $ be a compact subgroup of a locally compact group $G$. In this paper we define a convolution on $ M(G/H) $, the space of all complex bounded Radon measures on the homogeneous space G/H. Then we prove that the measure space $ M(G/H,…
We consider abstract inverse problems between infinite-dimensional Banach spaces. These inverse problems are typically nonlinear and ill-posed, making the inversion with limited and noisy measurements a delicate process. In this work, we…
We study the Radon transform in the plane in parallel geometry possibly undersampled in the angular variables. We study resolution, aliasing artifacts, and edge recovery.
In this paper we study set convergence aspects for Banach spaces of vector-valued measures with divergences (represented by measures or by functions) and applications. We consider a form of normal trace characterization to establish…
The main aim of this paper is to study multidimensional Bohr radii for holomorphic functions defined in complete Reinhardt domains in $\mathbb{C}^n$ with values in complex Banach spaces. More specifically, for holomorphic functions with…
A central objective in inverse problems arising in integral geometry is to understand the kernel characterization, inversion formulas, stability estimates, range characterization, and unique continuation properties of integral transforms.…
The classical tools which ensure the completeness of vector fields and second order differential equations for mechanical systems are revisited. Possible extensions in three directions are discussed: infinite dimensional Banach and Hilbert…
In this article, we study the multi-dimensional Bohr radii of holomorphic functions defined on the Banach sequence spaces with values in the Banach spaces. For the case of finite dimensional Banach spaces, we exhibit the exact asymptotic…
A diversity $\delta$ in $M$ is a function defined over every finite set of points of $M$ mapped onto $[0,\infty)$, with the properties that $\delta(X)=0$ if and only if $|X|\leq 1$ and $\delta(X\cup Y)\leq\delta(X\cup Z)+\delta(Z\cup Y)$,…
The aim of this note is to provide several variants of the diameter two properties for Banach spaces. We study such properties looking for the abundance of diametral points, which holds in the setting of Banach spaces with the Daugavet…
Quasi-invariant and pseudo-differentiable measures on a Banach space $X$ over a non-Archimedean locally compact infinite field with a non-trivial valuation are defined and constructed. Measures are considered with values in $\bf R$.…
We present a formalisation of the existence and uniqueness theorems of integral curves of vector fields on Banach manifolds in the Lean theorem prover. First, we formalize properties of differential equations on Banach spaces (the…
Having been unclear how to define that a domain is strictly pseudoconvex in the infinite-dimensional setting, we develop a general theory having Banach spaces in mind. We first focus on finite dimension and eliminate the need of two degrees…
Let M be an analytic manifold modelled on an ultrametric Banach space over a complete ultrametric field. Let f be an analytic diffeomorphism from M onto itself and p be a fixed point of f. We discuss invariant manifolds around p, like…
In this paper we give necessary and sufficient conditions for the norm on an infinite dimensional Banach space to be sub differentiable, for various classes of Bananch spaces.