For a locally compact group G, the measure convolution algebra M(G) carries a natural coproduct. In previous work, we showed that the canonical predual C0(G) of M(G) is the unique predual which makes both the product and the coproduct on M(G) weak∗-continuous. Given a discrete semigroup S, the convolution algebra l(S) also carries a coproduct. In this paper we examine preduals for l(S) making b...

Previously, idempotent methods have been found to be extremely fast for solution of dynamic programming equations associated with deterministic control problems. The original methods exploited the idempotent (e.g., max-plus) linearity of the associated semigroup operator. However, it is now known that the curse-of-dimensionality-free idempotent methods do not require this linearity. Instead, it...

We present a simple approach to study the one–dimensional pressureless Euler system via adhesion dynamics in the Wasserstein space P2(R) of probability measures with finite quadratic moments. Starting from a discrete system of a finite number of “sticky” particles, we obtain new explicit estimates of the solution in terms of the initial mass and momentum and we are able to construct an evolutio...