Related papers: The Vitali Covering Theorem in the Weihrauch Latti…

This paper classifies different fragments of the Galvin-Prikry theorem, an infinite dimensional generalization of Ramsey's theorem, in terms of their uniform computational content (Weihrauch degree). It can be seen as a continuation of…

We provide a self-contained introduction into Weihrauch complexity and its applications to computable analysis. This includes a survey on some classification results and a discussion of the relation to other approaches.

We prove a sharpened version of a conjecture of Dong-Mason about lattice subalgebras of a strongly regular vertex operator algebra $V$, and give some applications. These include the existence of a canonical conformal subVOA $W\otimes…

One of the most beautiful results in the integral representation theory of finite groups is a theorem of A. Weiss that detects a permutation $R$-lattice for the finite $p$-group $G$ in terms of the restriction to a normal subgroup $N$ and…

We discuss possible generalizations of Vitali convergence theorem when the source and the target are Banach analytic manifolds. These results are then applied to study behavior of holomorphic mappings between Banach analytic manifolds.…

The first part of the present article consists in a survey about the dynamical constructive method designed using dynamical theories and dynamical algebraic structures. Dynamical methods uncovers a hidden computational content for numerous…

[REVISED VERSION] The aim of this paper is to state a sharp version of the K\"onig supremum theorem, an equivalent reformulation of the Hahn--Banach theorem. We apply it to derive statements of the Lagrange multipliers, Karush-Kuhn-Tucker…

In his 1999 preprint "Universal Lie Algebra", P. Vogel put forward a hypothesis on the existence of a universal Lie algebra. Although this hypothesis remains open, it is known that many quantities in Lie theory admit universal descriptions.…

This paper studies existence and uniqueness of solutions to generalized Volterra integral equations. Since our proof for existence and uniqueness does not make use of Banach fixed point theorem unlike the previous papers focused on this…

We introduce an operator on problems in Weihrauch complexity, which we call the inverse limit, and which corresponds to an infinite compositional product. This operation arises naturally whenever one implements algorithms that produce a…

We establish a sharp upper bound for the bottom spectrum of the Beltrami Laplacian on universal covers of closed Riemannian manifolds with scalar curvature lower bound. Moreover, we prove a scalar curvature rigidity theorem when this bound…

For a map of the unit interval with an indifferent fixed point, we prove an upper bound for the variance of all observables of $n$ variables $K:[0,1]^n\to\R$ which are componentwise Lipschitz. The proof is based on coupling and decay of…

We prove a local limit theorem for Lipschitz continuous observables on a weakly coupled lattice of piecewise expanding interval maps. The core of the paper is a proof that the spectral radii of the Fourier-transfer operators for such a…

This paper is concerned with the concept of linear repetitivity in the theory of tilings. We prove a general uniform subadditive ergodic theorem for linearly repetitive tilings. This theorem unifies and extends various known (sub)additive…

We introduce a concept of approximately invertible elements in non-unital normed algebras which is, on one side, a natural generalization of invertibility when having approximate identities at hand, and, on the other side, it is a direct…

We study the complexity of the following related computational tasks concerning a fixed countable graph G: 1. Does a countable graph H provided as input have a(n induced) subgraph isomorphic to G? 2. Given a countable graph H that has a(n…

In the paper, we improve our earlier results concerning the existence, uniqueness and differentiability of a global implicit function. Some application to a Cauchy problem for an integro-differential Volterra system of nonconvolution type,…

We investigate the representation of lattices as sublattices of the lattice of all convex subsets (intervals) of a linearly ordered set $(X,\le)$. We introduce the purely lattice-theoretic notion of a \textit{loc-lattice} and prove that…

We show that a conceptually simple covering technique has surprisingly rich applications to density theorems and conjectures on patterns in sets involving set differences. These applications fall into three categories: (i) analogues of…

We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and…