Two hyperbolic Schwarz lemmas

Sharp Schwarz-type Lemmas for the Spectral Unit Ball

We provide generalisations of two Schwarz-type lemmas — the first a result of Globevnik and the other due to Ransford and White — for holomorphic mappings into the spectral unit ball. The first concerns mappings of the unit disc in C into the spectral unit ball, while the second concerns self-mappings. The aforementioned results apply to holomorphic mappings that map the origin to the origin. W...

Additive Schwarz Methods for Hyperbolic Equations 5153

Schwarz-pick-type Estimates Forthe Hyperbolic Derivative

Additive Schwarz Methods for Hyperbolic Equations

In recent years there has been gratifying progress in the development of domain decomposition algorithms for symmetric and nonsymmetric elliptic problems and even some inde nite problems Many methods possess the attractive property that the convergence rate is optimal i e independent of the size of the discrete problem and of the number of subdomains or within a polylog factor of optimal There ...

Two lemmas that changed general equilibrium theory