Arne Stray

ON INTERPOLATING FUNCTIONS WITH MINIMAL NORM

Let Hx denote the Banach algebra of bounded analytic functions in the unit disc (z: \z\ 1 if h e H°° and h # 0. An application of this result to the theory of best approximation is given.

Interpolating sequences and the Nevanlinna Pick problem

The extremal solutions to the Nevanlinna Pick problem are studied. If there is more than one solution, Nevanlinna showed that all extremal solutions are inner functions. With some extra information on the interpolation data we find that the extremal solutions are Blaschke products whose zeroes form a finite union of interpolating sequences.

Mergelyan type theorems for some function spaces

Let

Simultaneous approximation in function spaces

F

Blaschke products and Nevanlinna-Pick interpolation

be a relatively closed subset of the unit disc

Restrictions of the disc algebra described locally

D

Spaces of Analytic Functions

. If

Approximation and interpolation.

A

Minimal interpolation by Blaschke products

is any of the Hardy spaces

Interpolating Blaschke products.

H^p(D)