Resumen de Functional commutant lifting and interpolation on generalized analytic polyhedra,

Calin-Grigore Ambrozie

• We prove that for every generalized analytic polyhedron there exists a functional Hilbert space enabling the use of the commutant lifting technique for interpolation problems. This applies in particular to Caratheodory-Fejer type interpolation problems for bounded anaytic functions of several variables. The existence of the fractional transform - type solutions is then characterized in terms of positivity conditions. We show by a concrete example how to obtain such solutions.