Bounds and definablity over fields.
Let be an arbitrary commutative ring with identity, the general linear Lie algebra over , the diagonal subalgebra of . In case 2 is a unit of , all subalgebras of containing are determined and their derivations are given. In case 2 is not a unit partial results are given.
The Nevanlinna-Pick problem at the zeros of a Blaschke product B having a solution of norm smaller than one is studied. All its extremal solutions are invertible in the Douglas algebra D generated by B. If B is a finite product of sparse Blaschke products (Newman Blaschke products, Frostman Blaschke products) then so are all the extremal solutions. For a Blaschke product B a formula is given for the number C(B) such that if the NP-problem has a solution of norm smaller than C(B) then all its extremal...