A. I. Petrosyan

On Peak and Interpolation Sets of Algebras of Smooth Functions in the Polydisk

   It is proved, that any compact subset K of an interpolation Cm,a-smooth manifold on the distinguished boundary of unit polydisc Un is a peak set for the algebra of smooth functions Am-1,a(Un). Besides, the following interpolation result is obtained: For given f Cm(Tn) there is F Am-1,a(Un) with F|K = f|K. If given f belongs to Cm-1,a(Tn), then the interpolating function F can be chosen from (Un).