Ukrainian mathematical congress - 2009

Valentin Zagrebnov (Université Aix-Marseille II, Marseille, France)

Numerical range and quasi-sectorial contractions

We apply a method developed by Yu. Arlinskii to localize the numerical range of quasi-sectorial contractions semigroups. Our main theorem establishes a relation between the numerical range of quasi-sectorial contraction semigroups {exp(−tS)}, t > 0, and the maximal sectorial generators S. We also give a new prove of the rate O(1/n) for the operator-norm Euler formula approximation for this class of semigroups.

This is joint work with Yu. Arlinskii.