in this paper, we generalize some transfer theorems.~in particular, we derive one of the main results of gagola(contemp math 524:49--60, 2010) from our results.

We present a new technique to obtain polynomial decay estimates for the matrix coefficients of unitary operators. Our approach, based on commutator methods, applies nets operators, representations topological groups, and operators given by evolution group self-adjoint operator or powers operator. results are illustrated with wide range examples in quantum mechanics dynamical systems, as instanc...

The class of commutator-free Magnus integrators is known to provide a favourable alternative to standard Magnus integrators, in particular for large-scale applications arising in the time integration of non-autonomous linear evolution equations. A high-order commutator-free Magnus integrator is given by a composition of several exponentials that comprise certain linear combinations of the value...

The generators of the Poincaré symmetry of scalar electrodynam-ics are quantized in the functional Schrödinger representation. We show that the factor ordering which corresponds to (minimal) Dirac quantization preserves the Poincaré algebra, but (minimal) reduced quantization does not. In the latter, there is a van Hove anomaly in the boost-boost commutator, which we evaluate explicitly to lowe...

All extremal solutions of the truncated L-problem of moments in two real variables , with support contained in a given compact set, are described as characteristic functions of semi-algebraic sets given by a single polynomial inequality. An exponential kernel, arising as the determinantal function of a naturally associated hyponormal operator with rank-one self-commutator, provides a natural de...

Charles Sims has asked whether or not, for a free group F , the lower central subgroup γn(F ) coincides with the normal closure in F of the set of basic commutators of weight n. In this paper, we will show that Sims’ question has a positive answer when n = 5. The longest part of the proof is showing that this is true when F has rank 3. Once this is known, the results for higher ranks follow fai...

Let Mb be the operator of pointwise multiplication by b, that is Mb f = bf . Set [A,B] = AB−BA. The Reisz potentials are the operators Rα f(x) = ∫ f(x− y) dy |y|α , 0 < α < 1. They map L 7→ L, for 1 − α + 1 q = 1 p , a fact we shall take for granted in this paper. A Theorem of Chanillo MR84j:42027 [6] states that one has the equivalence ‖[Mb,Rα]‖p→q ≃ ‖b‖BMO with the later norm being that of th...

Two new measures to assess spatial ability are presented: the mental cutting test “Schnitte” (Fay & Quaiser-Pohl, 1999; English version: Fay, Quaiser-Pohl, & Rönicke, 2003), a test for selecting people with extraordinary spatial abilities, and the Picture Rotation Test (Hinze, 2002; Hinze & Quaiser-Pohl, 2003), a mental rotation test for preschool children. Both overcome some of the limits of t...

In this paper, we investigate some applications of commutator subgroups to homotopy groups and geometric groups. In particular, we show that the intersection subgroups of some canonical subgroups in certain link groups modulo their symmetric commutator subgroups are isomorphic to the (higher) homotopy groups. This gives a connection between links and homotopy groups. Similar results hold for br...