Restriction operators, balayage and doubly orthogonal systems of analytic functions
The authors prove qualitative results in a quite general situation in systems of analytic functions which are simultaneously orthogonal over each of two domains. They considered only Hilbert spaces of analytic functions, especially Bergman spaces. Such a problem has been studied previously in Hardy spaces. The situation is very different in Bergman spaces. From a more constructive point of view the authors study the Bergman restriction operator between the unit disk and a conpactly contained quadrature domain and show that the representing kernel of this operator is rational and it is expressible in terms of the polynomial equation of the boundary of the inner domain.
scientific article; zbMATH DE number 1915831
scientific article