THESIS
2016
Abstract
Let m be a nonnegative integer, {z
1,,z
n} be a sequence of distinct points in
open unit disk D of complex plane and {w
1,,w
n} be an arbitrary sequence of
complex numbers. The generalized Nevanlinna-Pick problem on Hardy Space H
2
of D is to find a condition that determines whether there exists a function f in
H
2 satisfying ❘❘f❘❘
2 ≤ 1 and f
(m)(z
i) = w
i for each i = 1,,n. In this thesis, the
necessary and sufficient conditions for this generalized Nevanlinna-Pick problem
are obtained by giving a constructive proof. Also, a formula for the minimal
norm among all the solutions and a form for such function are obtained. With
the utilization of minimal norm function, the analog of usual consequences in
the classical Nevanlinna-Pick problem can be deduced. This thesis also discu...[
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Let m be a nonnegative integer, {z
1,...,z
n} be a sequence of distinct points in
open unit disk D of complex plane and {w
1,...,w
n} be an arbitrary sequence of
complex numbers. The generalized Nevanlinna-Pick problem on Hardy Space H
2
of D is to find a condition that determines whether there exists a function f in
H
2 satisfying ❘❘f❘❘
2 ≤ 1 and f
(m)(z
i) = w
i for each i = 1,...,n. In this thesis, the
necessary and sufficient conditions for this generalized Nevanlinna-Pick problem
are obtained by giving a constructive proof. Also, a formula for the minimal
norm among all the solutions and a form for such function are obtained. With
the utilization of minimal norm function, the analog of usual consequences in
the classical Nevanlinna-Pick problem can be deduced. This thesis also discusses
another generalized Nevanlinna-Pick problem, which would lead to a possibility
of solving the Nevanlinna-Pick problem with boundary data on H
2.
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