Convolution lattices

An equivalence functor between local vector lattices and vector lattices

We call a local vector lattice any vector lattice with a distinguished positive strong unit and having exactly one maximal ideal (its radical). We provide a short study of local vector lattices. In this regards, some characterizations of local vector lattices are given. For instance, we prove that a vector lattice with a distinguished strong unit is local if and only if it is clean with non no-...

Torsional random walk statistics on lattices using convolution on crystallographic motion groups.

This paper presents a new algorithm for generating the conformational statistics of lattice polymer models. The inputs to the algorithm are the distributions of poses (positions and orientations) of reference frames attached to sequentially proximal bonds in the chain as it undergoes all possible torsional motions in the lattice. If z denotes the number of discrete torsional motions allowable a...

Convolution Equations on Lattices: Periodic Solutions with Values in a Prime Characteristic Field

These notes are inspired by the theory of cellular automata which targets, in particular, to provide a model for inter-cellular or inter-molecular interactions. A cellular automaton on a lattice Z or on a toric grid can be regarded as a convolution operator ∆a : f 7−→ f ∗a with kernel a concentrated in the nearest neighborhood of 0. In [Za] we gave a survey on the most studied cellular automata...

Weighted Convolution Measure Algebras Characterized by Convolution Algebras

The weighted semigroup algebra Mb (S, w) is studied via its identification with Mb (S) together with a weighted algebra product *w so that (Mb (S, w), *) is isometrically isomorphic to (Mb (S), *w). This identification enables us to study the relation between regularity and amenability of Mb (S, w) and Mb (S), and improve some old results from discrete to general case.

Convolution and Homogeneous Spaces