A Banach algebra is Arens-regular when all its continuous functionals are weakly almost periodic, in symbols A⁎=WAP(A). To identify the opposite behaviour, Granirer called a extremely non-Arens regular (enAr, for short) quotient A⁎/WAP(A) contains closed subspace that has A⁎ as quotient. In this paper we propose simplification and quantification of concept. We say r-enAr, with r≥1, there an iso...

We consider a nonlinear random walk which, in each time step, is free to choose its own transition probability within neighborhood (w.r.t. Wasserstein distance) of the fixed Lévy process. In analogy classical framework we show that, when passing from discrete continuous via scaling limit, this gives rise semigroup. explicitly compute generator semigroup and corresponding PDE as perturbation ini...

The wavelet dimension function for arbitrary real dilations is defined and used to address several questions involving the existence of MRA wavelets and well-localized wavelets for irrational dilations. The theory of quasi-affine frames for rational dilations and the existence of non-MSF wavelets for certain irrational dilations play an important role in this development. Expansive dilations ad...

Abstract We introduce a notion of sensitivity with respect to continuous real-valued bounded map which provides sufficient condition for transformation, acting on Baire metric space, exhibit generic subset points historic behavior (also known as irregular points). The applications this criterion recover, and extend, several theorems the genericity set, in addition yielding number new results, i...

Let Z be a Banach lattice endowed with positive cone C and an order-continuous norm j.j . Let G be a left-amenable semigroup of positive linear endomorphisms of Z . Then the positive fixed points Co of Z under G form a lattice cone, and their linear span Z0 is a Banach lattice under an order-continuous norm ||.||0 which agrees with |.| on Co. A counterexample shows that under the given conditio...

Semigroups whose congruences form a chain are often termed ∆-semigroups. The commutative ∆-semigroups were determined by Schein and by Tamura. A natural generalization of commutativity is permutativity: a semigroup is permutative if it satisfies a non-identity permutational identity. We completely determine the permutative ∆-semigroups. It turns out that there are only six noncommutative exampl...

This paper is concerned with the initial value problem for a strictly hyperbolic n n system of conservation laws in one space dimension: u t + F(u) x = 0; u(0; x) = u(x): () Each characteristic eld is assumed to be either linearly degenerate or genuinely nonlinear. We prove that there exists a domain D L 1 , containing all functions with suuciently small total variation, and a uniformly Lipschi...

Group equivariant operators are playing a more and relevant role in machine learning topological data analysis. In this paper, we present some new results concerning the construction of G-equivariant non-expansive (GENEOs) from space \(\Phi \) real-valued bounded continuous functions on X to itself. The represents our set data, while G is subgroup group all self-homeomorphisms X, representing i...