We use induction and interpolation techniques to prove that a composition operator induced by a map φ is bounded on the weighted Bergman space Aα(H) of the right half-plane if and only if φ fixes ∞ non-tangentially, and has a finite angular derivative λ there. We further prove that in this case the norm, essential norm, and spectral radius of the operator are all equal, and given by λ.

The essential point will be the equivalence of the norm of the error, which should be estimated, and a corresponding dual norm of the residual which only involves the given data of the problem and the computed numerical solution. This equivalence is a consequence of the stability of the infinite dimensional variational problem. Thus, in a posteriori error analysis the situation is quite differe...

for calculation of the displacements of points in micro geodesy networks, it is essential to discover stable and unstable points. without knowing stable points, calculated displacements are due to datum deficiency. in this case, calculated displacements are not valid. there are two methods to discover stable and unstable points: a-congruency robust method b- l1 norm minimization in this study t...