Pick interpolation and invariant functions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F25%3A00144603" target="_blank" >RIV/00216224:14310/25:00144603 - isvavai.cz</a>
Result on the web
<a href="https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/annales-polonici-mathematici/online/116085/pick-interpolation-and-invariant-functions" target="_blank" >https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/annales-polonici-mathematici/online/116085/pick-interpolation-and-invariant-functions</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/ap250220-2-6" target="_blank" >10.4064/ap250220-2-6</a>

Result language
angličtina
Original language name
Pick interpolation and invariant functions
Original language description
We establish a connection between Pick bodies and invariant functions. We demonstrate that an invariant function can be associated with any Pick body, which determines the solvability of a given Pick interpolation problem and generalizes the Carath & eacute;odory pseudodistance. A complete description of this invariant function is provided for the open unit disc, and it is shown that it leads to another invariant function which can be regarded as a generalized Lempert function. It is also proved that these two invariant functions are equal if certain geodesics can be found. Lastly, we show that, in a very special case, a result analogous to Lempert's theorem holds for the bidisc and the tridisc.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GC22-15012J" target="_blank" >GC22-15012J: Smooth and analytic regularity in CR geometry</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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