The infinitesimal generators of certain parameter groups

Wiener Integral Representations for Certain Semigroups Which Have Infinitesimal Generators with Matrix Coefficients

Generators and Relations for Certain Special Linear Groups

Several years ago I calculated presentations for several of the groups SL(2, R) where R is the ring of integers of a quadratic imaginary number field K = Q((—in)). The method used was extremely tedious and was never published. Recently, while checking these calculations, I discovered a much simpler approach to the problem which I will outline here. The interest in these calculations is consider...

Comparison of Markov processes via infinitesimal generators

We derive comparison results for Markov processes with respect to stochastic orderings induced by function classes. Our main result states that stochastic monotonicity of one process and comparability of the infinitesimal generators implies ordering of the processes. Unlike in previous work no boundedness assumptions on the function classes are needed anymore. We also present an integral versio...

On Landau’s type inequalities for infinitesimal generators∗

We consider Landau’s type inequalities of the form ‖Aku‖n ≤ Cn,k‖u‖n−k‖Anu‖k, u ∈ D(A), 0 < k < n, where A is the infinitesimal generator of either a strongly continuous semigroup or a strongly continuous cosine function of linear contractions on a Banach space X. The constants Cn,k are computed for n ≤ 6.

Infinitesimal Presentations of the Torelli Groups

Contents 1. Introduction 597 2. Braid groups in positive genus 601 3. Relative completion of mapping class groups 603 4. Mixed Hodge structures on Torelli groups 608 5. Review of continuous cohomology 613 6. Remarks on the representations of sp g 616 7. Continuous cohomology of Torelli groups 618 8. The lower central series quotients of a surface group 621 9. The action of t 1 g on p g 623 10. ...