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Extremal functions of the Nevanlinna-Pick problem and Douglas algebras

V. Tolokonnikov (1993)

Studia Mathematica

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...

Factorization properties of Krull monoids with infinite class group

Wolfgang Hassler (2002)

Colloquium Mathematicae

For a non-unit a of an atomic monoid H we call L H ( a ) = k | a = u . . . u k w i t h i r r e d u c i b l e u i H the set of lengths of a. Let H be a Krull monoid with infinite divisor class group such that each divisor class is the sum of a bounded number of prime divisor classes of H. We investigate factorization properties of H and show that H has sets of lengths containing large gaps. Finally we apply this result to finitely generated algebras over perfect fields with infinite divisor class group.

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