Local objects in the theory of Toeplitz operators

This paper is aimed at the local theory of Toeplitz operators including harmonic extension, harmonic approximation and finite section method.     

Algebras generated by idempotents and the symbol calculus for singular integral operators

It is proved that in Banach algebras generated by two idempotents and, perhaps, by a certain flip operator the standard identity F₄ is fulfilled. The maximal ideal space of such algebras is determined and the corresponding symbol is given. By means of local techniques these results are applied to obtain a symbol calculus for singular integral operators with Carleman shift (changing the orientation) in weighted Banach spaces.     

Quantized electrons and holes in tellurium surfaces

A calculation has been made for surface phonons at the (001) surface of some fcc and bcc transition metals. A model consisting of first and second neighbor central interactions together with angle bending forces is used. The general harmonic approximation is used. A least mean square fit of the bulk phonon spectrum determines the parameters characterizing the interactions. Specific results have been obtained for surface phonons of Pt, Pd, Cu and Ag as well as Fe and W. The effect of varying the force constant near the surface is also reported showing the possibility for the existence of soft surface modes which may account for superstructures.     

On operator split technique for the time integration within finite strain viscoplasticity in explicit FEM

In this contribution, the operator split technique is applied to the time integration within viscoplasticity for explicit FEM. As an example, the finite strain viscoplastic material model of Shutov and Kreißig is analyzed. In the new solution scheme, some evolution equations are solved using an explicit update formula for implicit time stepping. The solution procedure is split into three steps: an elastic predictor and two viscoplastic corrector steps. Aspects of accuracy and stability of the algorithm are discussed. As shown, the proposed method is superior compared to a fully explicit integration of evolution equations. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)