Section: New Results
Best constrained analytic approximation
Participants : Laurent Baratchart, Sylvain Chevillard, Juliette Leblond, Dmitry Ponomarev, Elodie Pozzi.
This work is performed in collaboration with Jonathan Partington (Univ. Leeds, UK).
Continuing effort is being paid by the team to
carry over the solution to bounded extremal problems of section
3.3.1
to various settings.
We mentioned already in section
6.2
the extension to 2-D diffusion equations with variable
conductivity for the determination of free boundaries in
plasma control and the development of
a generalized Hardy class theory.
We also investigate the ordinary Laplacian in
Still, questions about the behaviour of solutions to the
standard bounded extremal problems
In another connection, weighted composition operators on Lebesgue, Sobolev, and Hardy spaces appear in changes of variables while expressing conformal equivalence of plane domains. A universality property related to the existence of invariant subspaces for these important classes of operators has been established in [19] . Additional density properties also allow one to handle some of their dynamical aspects (like cyclicity).