Functional commutant lifting and interpolation on generalized analytic polyhedra,

• Autores: Calin-Grigore Ambrozie
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 34, Nº 2, 2008, págs. 519-544
• Idioma: inglés
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• Resumen

  • 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.