On eventual compactness of collisionless kinetic semigroups with velocities bounded away from zero

Incremental Gradient Algorithms with Stepsizes Bounded Away from Zero

We consider the class of incremental gradient methods for minimizing a sum of continuously differentiable functions. An important novel feature of our analysis is that the stepsizes are kept bounded away from zero. We derive the first convergence results of any kind for this computationally important case. In particular, we show that a certain ε-approximate solution can be obtained and establis...

Compactness of Schrödinger semigroups

This paper is concerned with emptyness of the essential spectrum, or equivalently compactness of the semigroup, for perturbations of selfadjoint operators that are bounded below (on an L2-space). For perturbations by a (nonnegative) potential we obtain a simple criterion for compactness of the semigroup in terms of relative compactness of the operators of multiplication with characteristic func...

Compactness of Systems of Equations on Completely Regular Semigroups

A semigroup S is said to have the compactness property, or CP for short, if each system of equations over a nite set of variables has an equivalent nite subsystem, that is, having exactly the same solutions in S. We prove that a completely 0-simple semigroup S satis es CP if and only if the group G in a Rees matrix representation S = M0(I; G; ;P) satis es this property. Further, a variety of co...

Bounded Semigroups of Matrices

In this note are proved two conjectures of Daubechies and Lagarias. The first asserts that if Z is a bounded set of matrices such that all left infinite products converge, then 8 generates a bounded semigroup. The second asserts the equality of two differently defined joint spectral radii for a bounded set of matrices. One definition involves the conventional spectral radius, and one involves t...

Functions of bounded variation on idempotent semigroups