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

It is proved, that any compact subset K of an
interpolation C^{m,a}-smooth manifold on the
distinguished boundary of unit polydisc **U**^{n} is a
peak set for the algebra of smooth functions A^{m-1,a}(**U**^{n}). Besides, the following interpolation result is
obtained: For given f Î
*C*^{m}(**T**^{n}) there is F Î
A^{m-1,a}(**U**^{n}) with F|_{K }= f|_{K}. If
given f belongs to *C*^{m-1,a}(**T**^{n}), then the interpolating function F can
be chosen from
(**U**^{n}).