🚀 go-pugleaf

	Let m(z) be an inner function defined on the unit disc D, and
let z_1,...,z_n be finitely many points on D. It is known that there
exists a rational inner function m_f(z) which interpolates m(z) at
z_1,..,z_n (This is a classical result in Nevallina-Pick interpolation
theory).
	My question is about the parametrization of all such m_f's? 
Does anybody know anything about 

	(1) parametrization of all such m_f's? 

	(2) given N, is there an m_f of order N?

Remarks: The parametrization of all analytic functions with norm <= 1
and satisfying the above interpolation conditions is known.
Furthermore if we know the definition of the function m(z) and the
numerical values of points z_1,...,z_n then question (2) can be
answered by reducing it to a linear algebra problem and checking
whether  a system of equations has a solution or not. But I don't know
whether (2) holds for all sufficently large N values (or for N > 2*n).

	O.Toker