Pseudo-Taylor expansions and the Carathéodory-Fejér problem

Details Pseudo-Taylor expansions and the Carathéodory-Fejér problem Pseudo-Taylor expansions and the Carathéodory-Fejér problem

2011-01-06

arxiv.org/abs/1101.1251v1

Mathematics

Complex Variables

18 pages

Scientific paper

We give a new solvability criterion for the boundary Carath\'{e}odory-Fej\'{e}r problem: given a point $x \in \R$ and, a finite set of target values $a^0,a^1,...,a^n \in \R$, to construct a function $f$ in the Pick class such that the limit of $f^{(k)}(z)/k!$ as $z \to x$ nontangentially in the upper half plane is $a^k$ for $k= 0,1,...,n$. The criterion is in terms of positivity of an associated Hankel matrix. The proof is based on a reduction method due to Julia and Nevanlinna.

Affiliated with

Also associated with

No associations

Rating

Pseudo-Taylor expansions and the Carathéodory-Fejér problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Pseudo-Taylor expansions and the Carathéodory-Fejér problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Pseudo-Taylor expansions and the Carathéodory-Fejér problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-399895