Operator-Norm Approximation of Semigroups by Quasi-sectorial Contractions

Quasi-sectorial contractions

We revise the notion of the quasi-sectorial contractions. Our main theorem establishes a relation between semigroups of quasi-sectorial contractions and a class of m−sectorial generators. We discuss a relevance of this kind of contractions to the theory of operator-norm approximations of strongly continuous semigroups.

Numerical Range and Quasi - Sectorial Contractions

We apply a method developed by one of the authors, see [1], 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: e...

Approximation of Semigroups and Related Operator Functions by Resolvent Series

Abstract. We consider the approximation of semigroups e and of the functions φj(τA) that appear in exponential integrators by resolvent series. The interesting fact is that the resolvent series expresses the operator functions e and φj(τA), respectively, in efficiently computable terms. This is important for semigroups, where the new approximation is different from well-known approximations by ...

Generation of Equicontinuous Semigroups by Hermitian and Sectorial Operators. I

Operator Holes and Extensions of Sectorial Operators and Dual Pairs of Contractions

A description of the set of m-sectorial extensions of a dual pair {A1, A2} of nonnegative operators is obtained. Some classes of nonaccretive extensions of the dual pair {A1, A2} are described too. Both problems are reduced to similar problems for a dual pair {T1, T2} of nondensely defined symmetric contractions Tj = (I−Aj)(I+Aj), j ∈ {1, 2}. In turn these problems are reduced to the investigat...