Stability and Convergence of Product Formulas for Operator Matrices

We present easy to verify conditions implying stability estimates for operator matrix splittings which ensure convergence of the associated Trotter, Strang and weighted product formulas. The results are applied to inhomogeneous abstract Cauchy problems and to boundary feedback systems.Comment: to appear in Integral Equations and Operator Theory (ISSN: 1420-8989

On locally graded groups with a word whose values are Engel

Let m, n be positive integers, v a multilinear commutator word and w = v^m. We prove that if G is a locally graded group in which all w-values are n-Engel, then the verbal subgroup w(G) is locally nilpotent.Comment: to appear in "Proceedings of the Edinburgh Mathematical Society

On prolongations of contact manifolds

We apply spectral sequences to derive both an obstruction to the existence of $n$-fold prolongations and a topological classification. Prolongations have been used in the literature in an attempt to prove that every Engel structure on $M\times\mathbb{S}^1$ with characteristic line field tangent to the fibers is determined by the contact structure induced on a cross section and the twisting of the Engel structure along the fibers. Our results show that this statement needs some modification: to classify the diffeomorphism type of the Engel structure we additionally have to fix a class in the first cohomology of $M$.Comment: 8 pages; corrected an error in Corollary 4.1., this version will appear in Proc. of the Amer. Math. So

Words of Engel type are concise in residually finite groups

Given a group-word w and a group G, the verbal subgroup w(G) is the one generated by all w-values in G. The word w is said to be concise if w(G) is finite whenever the set of w-values in G is finite. In the sixties P. Hall asked whether every word is concise but later Ivanov answered this question in the negative. On the other hand, Hall\u2019s question remains wide open in the class of residually finite groups. In the present article we show that various generalizations of the Engel word are concise in residually finite groups