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 Î
Cm(Tn) there is F Î
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).