Related papers: Differentiable mappings on products with different…

Examples of differentiable mappings into real or complex topological vector spaces with specific properties are given, which illustrate the differences between differential calculus in the locally convex and the non-locally convex case. In…

In this paper, we introduce restricted products for families of locally convex spaces and formulate criteria ensuring that mappings into such products are continuous or smooth. As a special case, can define restricted products of weighted…

We provide sufficient conditions for the existence of a strong derivable map and calculate its derivative by employing a result in our previous work on strong derivability of maps arising by functional calculus of an unbounded scalar type…

In this paper, the concept of selective real manifolds is extended. It is proved that the product of two selective Banach manifolds is a selective Banach manifold. The notion of the $\alpha$--level differentiation of the mappings between…

Usually, for extension of local maps, one uses multiplication by so called bump functions. However, majority of infinite-dimensional linear topological spaces do not have smooth bump functions. Therefore, in \cite{BR} we suggested a new…

Let $E$ be a locally convex space, $U\subseteq\mathbb{R}^n$ as well as $V\subseteq\mathbb{R}^m$ be open and $k,l\in\mathbb{N}_0\cup\left\{\infty\right\}$. Locally convex spaces $C^{k,l}(U\times V,E)$ of functions with different degrees of…

The question of extension of locally defined maps to the entire space arises in many problems of analysis (e.g., local linearization of functional equations). A known classical method of extension of smooth local maps on Banach spaces uses…

We present an axiomatic approach to finite- and infinite-dimensional differential calculus over arbitrary infinite fields (and, more generally, suitable rings). The corresponding basic theory of manifolds and Lie groups is developed.…

It is shown that a Banach space with locally uniformly convex dual admits an equivalent norm which is itself locally uniformly convex. It follows that on any such space all continuous real-valued functions may be uniformly approximated by…

We prove various results in infinite-dimensional differential calculus which relate differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: 1. in the…

Given two Banach function spaces we study the pointwise product space E.F, especially for the case that the pointwise product of their unit balls is again convex. We then give conditions on when the pointwise product E . M(E, F)=F, where…

We prove a version of the Stokes formula for differential forms on locally convex spaces. The main tool used for proving this formula is the surface layer theorem proved in another paper by the author. Moreover, for differential forms of a…

A notion of differentiability is being proposed for maps between Wasserstein spaces of order 2 of smooth, connected and complete Riemannian manifolds. Due to the nature of the tangent space construction on Wasserstein spaces, we only give a…

This paper develops a geometric approach of variational analysis for the case of convex objects considered in locally convex topological spaces and also in Banach space settings. Besides deriving in this way new results of convex calculus,…

We investigate the relationship between the existence of directional derivatives for cone-convex functions with values in a Banach space Y and isomorphisms between Y and c0.

Here we consider a perturbation of continuous mappings on Banach spaces and investigate their image under various conditions. Consequently, we study the solvability of some classes of equations and inclusions. For these, we start by the…

In this paper, we investigate some properties of the Mordukhovich derivatives of the normalized duality mapping in Banach spaces. For the underlying spaces, we consider three cases: uniformly convex and uniformly smooth Banach space lp;…

We define notions of differentiability for maps from and to the space of persistence barcodes. Inspired by the theory of diffeological spaces, the proposed framework uses lifts to the space of ordered barcodes, from which derivatives can be…

In this work, various versions of the so-called Omega-Lemma are provided, which ensure differentiability properties of pushforwrds between spaces of C^r-sections (or compactly supported C^r-sections) in vector bundles over…

We give a complete characterization of those $f: [0,1] \to X$ (where $X$ is a Banach space which admits an equivalent Fr\'echet smooth norm) which allow an equivalent $C^2$ parametrization. For $X=\R$, a characterization is well-known.…