The boundary Carathéodory–Fejér interpolation problem
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- Professor Jim Agler
- Dr Zinaida Lykova
- Professor Nicholas Young
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| Author(s) | | Agler J, Lykova ZA, Young NJ |
| Publication type | | Article |
| Journal | | Journal of Mathematical Analysis and Applications |
| Year | | 2011 |
| Volume | | 382 |
| Issue | | |
| Pages | | 645-662 |
| ISSN (print) | | 0022-247X |
| ISSN (electronic) | | 1096-0813 |
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| Full text is available for this publication: |
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| We give an elementary proof of a solvability criterion for the {\em boundary Carath\'{e}odory-Fej\'{e}r problem}: given a point $x \in \R$ and, a finite set of target values, to construct a function $f$ in the Pick class such that the first few derivatives of $f$ take on the prescribed target values at $x$. We also derive a linear fractional parametrization of the set of solutions of the interpolation problem. The proofs are based on a reduction method due to Julia and Nevanlinna. |
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| Publisher | | Academic Press |
| URL | | http://dx.doi.org/10.1016/j.jmaa.2011.04.071 |
| DOI | | 10.1016/j.jmaa.2011.04.071 |
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