Related papers: Functionally $\sigma$-discrete mappings and a gene…
This note aims to highlight the link between representable functionals and derivations on a Banach quasi *-algebra, i.e. a mathematical structure that can be seen as the completion of a normed *-algebra in the case the multiplication is…
We use discrete holomorphic polynomials to prove that, given a refining sequence of critical maps of a Riemann surface, any holomorphic function can be approximated by a converging sequence of discrete holomorphic functions.
Properties of Lipschitz and d.c. surfaces of finite codimension in a Banach space, and properties of generated $\sigma$-ideals are studied. These $\sigma$-ideals naturally appear in the differentiation theory and in the abstract…
The study of the global mapping properties of arbitrary Dirichlet L-functions is undertaken. The results are applied to the proof of the Generalized Riemann Hypothesis.
Based on a refinement of the notion of internal sets in Colombeau's theory, so-called strongly internal sets, we introduce the space of generalized smooth functions, a maximal extension of Colombeau generalized functions. Generalized smooth…
The concept of generalized partial-slice monogenic functions has been recently introduced to include the two theories of monogenic functions and of slice monogenic functions over Clifford algebras. The main purpose of this article is to…
A distance-squared function is one of the most significant functions in the application of singularity theory to differential geometry. In this paper, we define naturally extended mappings of distance-squared functions, wherein each…
We consider the space of non-expansive mappings on a bounded, closed and convex subset of a Banach space equipped with the metric of uni- form convergence. We show that the set of strict contractions is a {\sigma}-porous subset.
It is known that smooth bump functions are absent in the majority of infinite-dimensional Banach spaces. This is an obstacle in the development of local analysis, in particular in the questions of extending local maps onto the whole space.…
The Hahn-Banach theorem is an extension theorem for linear functionals which preserves certain properties. Specifically, if a linear functional is defined on a subspace of a real vector space which is dominated by a sublinear functional on…
Let \Sigma be a compact Riemann surface with n distinguished points p_1,...,p_n. We prove that the set of n-tuples (\phi_1,...,\phi_n) of univalent mappings \phi_i from the open unit disc into \Sigma mapping 0 to p_i, with non-overlapping…
We give a direct non-abstract proof of the Spectral Mapping Theorem for the Helffer-Sj\"ostrand functional calculus for linear operators on Banach spaces with real spectra and consequently give a new non-abstract direct proof for the…
A topological description of various generalized function algebras over corresponding basic locally convex algebras is given. The framework consists of algebras of sequences with appropriate ultra(pseudo)metrics defined by sequences of…
We investigate the existence of subinvariant metric functionals for commuting families of nonexpansive mappings in noncompact subsets of Banach spaces. Our findings underscore the practicality of metric functionals when searching for fixed…
We introduce a modified version of the Whitney extension operators for collections of functions from a closed subset of $\mathbb{R}^n$ into scales of Banach spaces with smoothing operators. We prove an extension theorem for collections…
We develop a linear theory of discrete complex analysis on general quad-graphs, continuing and extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete complex analysis on rhombic quad-graphs. Our approach based on…
We study the class of compact convex subsets of a topological vector space which admits a strictly convex and lower semicontinuous function. We prove that such a compact set is embeddable in a strictly convex dual Banach space endowed with…
Recently, versions of neural networks with infinite-dimensional affine operators inside the computational units (``neural operator'' networks) have been applied to learn solutions to differential equations. To enable practical computations,…
Motivated by extending the functional stochastic calculus, to important functionals to which it does not apply, a notion of functional derivative along a curve is introduced. This new setting is developed by incorporating path-dependent…
In this article we go on to discuss about various proper extensions of Kannan's two different fixed point theorems, introducing the new concept of $\sigma_c$-function; which is independent of the three notions of simulation function,…