Related papers: Coinductive properties of Lipschitz functions on s…
Coinductive reasoning about infinitary structures such as streams is widely applicable. However, practical frameworks for developing coinductive proofs and finding reasoning principles that help structure such proofs remain a challenge,…
This paper is about certain string-to-string functions, called the polyregular functions. These are like the regular string-to-string functions, except that they can have polynomial (and not just linear) growth. The class has four…
The classical Hahn-Banach theorem is based on a successive point-by-point procedure of extending bounded linear functionals. In the setting of a general metric domain, the conditions are less restrictive and the extension is only required…
On a non-compact, smooth, connected, boundaryless, complete Riemannian manifold $(M,g)$, one can define its ideal boundary by rays (or equivalently, Busemann functions). From the viewpoint of Mather theory, boundary elements could be…
Metric coinduction is a form of coinduction that can be used to establish properties of objects constructed as a limit of finite approximations. One can prove a coinduction step showing that some property is preserved by one step of the…
In 2009, Hancock, Pattinson and Ghani gave a coalgebraic characterisation of stream processors $A^\mathbb{N} \to B^\mathbb{N}$ drawing on ideas of Brouwerian constructivism. Their stream processors have an intensional character; in this…
Inspired by the results obtained in \cite{SR}, in this work, we develop techniques to handle the contraction property for weak normalization and Lipschitz saturation of algebras for the following types of algebras: universally injective,…
This work studies the typical behavior of random integer-valued Lipschitz functions on expander graphs with sufficiently good expansion. We consider two families of functions: M-Lipschitz functions (functions that change by at most M along…
Like termination, confluence is a central property of rewrite systems. Unlike for termination, however, there exists no known complexity hierarchy for confluence. In this paper we investigate whether the decreasing diagrams technique can be…
We show that sweeping processes with possibly non-convex prox-regular constraints generate a strongly continuous input-output mapping in the space of absolutely continuous functions. Under additional smoothness assumptions on the constraint…
We give an explicit coinduction principle for recursively-defined stochastic processes. The principle applies to any closed property, not just equality, and works even when solutions are not unique. The rule encapsulates low-level analytic…
We prove that the Schweitzer complex is elliptic and its cohomologies define cohomological functors. As applications, we obtain finite dimensionality, a version of Serre duality, restrictions of the behaviour of cohomology in small…
We consider a countably generated and uniformly closed algebra of bounded functions. We assume that there is a lower semicontinuous, with respect to the supremum norm, quadratic form and that normal contractions operate in a certain sense.…
Certain operator algebras A on a Hilbert space have the property that every densely defined linear transformation commuting with A is closable. Such algebras are said to have the closability property. They are important in the study of the…
We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent $\alpha$, with $0<\alpha<1$, in the vicinity of an exceptional boundary point where all such functions…
We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool…
We show that there can be no algorithm to decide whether infinite recursively described acyclic aspherical 2-complexes are contractible. We construct such a complex that is contractible if and only if the Collatz conjecture holds.
It was already known that a p-adic, locally Lipschitz continuous semi-algebraic function is piecewise Lipschitz continuous, where the pieces can be taken semi-algebraic. We prove that if the function has locally Lipschitz constant 1, then…
The paper is devoted to generic translation flows corresponding to Abelian differentials with one zero of order two on flat surfaces of genus two. These flows are weakly mixing by the Avila-Forni theorem. Our main result gives first…
We establish the strong unique continuation property of fractional orders of linear elliptic equations with Lipschitz coefficients by establishing monotonicity of some Almgren-type frequency functional via an extension procedure.