We systematically analyze regularization of different kinds of ultradistribution semigroups and sines, in general, with nondensely defined generators and contemplate several known results concerning the regularization of Gevrey type ultradistribution semigroups. We prove that, for every closed linear operator A which generates an ultradistribution semigroup (sine), there exists a bounded inject...

The interaction of automatic semigroups and Bruck–Reilly extensions is studied. It is proved that every automatic Bruck–Reilly extension has an automatic base semigroup. This result is then applied to answer negatively the question of Andrade et al. on whether automatic structures for Bruck–Reilly extensions of groups are characterized by the fellow traveller property. An example is exhibited t...

We derive the actions for type II Green-Schwarz strings up to second order in the fermions, for general bosonic backgrounds. We base our work on the so-called normal coordinate expansion. The resulting actions are κ-symmetric and, for the case of surviving background supersymmetries, supersymmetric. We first obtain the type IIa superstring action from the 11D supermembrane by double dimensional...

For a unital foundation topological *-semigroup S whose representations separate points of S, we show that the spectrum of the Fourier-Stieltjes algebra B(S) is a compact semitopological semigroup. We also calculate B(S) for several examples of S.

A numerical index is introduced for semigroups of completely positive maps of B(H) which generalizes the index of E0-semigroups. It is shown that the index of a unital completely positive semigroup agrees with the index of its dilation to an E0-semigroup, provided that the dilation is minimal. Introduction. We introduce a numerical index for semigroups P = {Pt : t ≥ 0} of normal completely posi...

Let S be a numerical semigroup with embedding dimension e(S), Frobenius number g(S), and type t(S). Put n(S) := Card(S ∩ {0, 1, . . . , g(S)}). A question of Wilf is shown to be equivalent to the statement that e(S)n(S) ≥ g(S)+1. This question is answered affirmatively if S is symmetric, pseudo-symmetric, or of maximal embedding dimension. The question is also answered affirmatively in the foll...

Abstract: If the system semigroup of a control system is a group, the system has the partition property, i.e., the reachable sets form a disjoint partition in the state space. The converse is not true in general. In this work we give sufficient conditions for the partition property for a family of discrete-time control systems on homogeneous spaces. We apply our results to Inverse Iteration sys...

Two different numerical methods for solving a non-self-adjoint evolution equation are compared in this paper. If the initial function lies in the domain of the operator, a recently proposed method that combines pseudospectral ideas and semigroup theory is shown to be considerably more accurate than a standard discretization method. One example is worked out in detail, but the methods used are o...

We consider fully discrete schemes for the one dimensional linear Schrödinger equation and analyze whether the classical dispersive properties of the continuous model are presented in these approximations. In particular Strichartz estimates and the local smoothing of the numerical solutions are analyzed. Using a backward Euler approximation of the linear semigroup we introduce a convergent sche...

We consider a fractional order integro-differential equation with a weakly singular convolution kernel. The equation with homogeneuos Dirichlet boundary conditions is reformulated as an abstract Cauchy problem, and well-posedness is verified in the context of linear semigroup theory. Then we formulate a continuous Galerkin method for the problem, and we prove stability estimates. These are then...