2-proper Holomorphic Images of Classical Cartan Domains
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F25%3AA0000203" target="_blank" >RIV/47813059:19610/25:A0000203 - isvavai.cz</a>
Výsledek na webu
<a href="https://www.iumj.indiana.edu/IUMJ/fulltext.php?artid=60290&year=2025&volume=74" target="_blank" >https://www.iumj.indiana.edu/IUMJ/fulltext.php?artid=60290&year=2025&volume=74</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1512/iumj.2025.74.60290" target="_blank" >10.1512/iumj.2025.74.60290</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
2-proper Holomorphic Images of Classical Cartan Domains
Popis výsledku v původním jazyce
Motivated by the way two special domains, namely the symmetrized bidisc and the tetrablock, could be defined as the images of 2-proper holomorphic images of classical Car-tan domains, we present a general approach to study 2-proper holomorphic images of bounded symmetric domains. We show some special properties of 2-proper holomorphic maps (such as the construction of some involutive automorphisms, etc.) and enlist possible domains (up to biholomorphisms) which arise as 2-proper holomorphic images of bounded symmetric domains. This leads us to a consideration of a new family of domains Ln for n >= 2. Let Ln be an irreducible classical Cartan domain of type IV (Lie ball) of dimension n, and Lambda(n) : L-n -> Lambda(n)(L-n) := L(n )be the natural proper holomorphic mapping of multiplicity 2. It turns out that L-2 and L-3 are biholomorphic to the symmetrized bidisc and the tetrablock, respectively. In this article, we study function geometric properties of the family {L-n : n >= 2} in a unified manner, and thus extend results of many earlier papers on analogous properties of the symmetrized bidisc and the tetrablock. We show that L-n cannot be exhausted by domains biholomorhic to some convex domains. Any proper holomorphic self-mapping of L-n is an automorphism for n >= 3. Moreover, the automorphism group Aut(L-n) is isomorphic to Aut(Ln-1), and L-n is inhomogeneous for n >= 2. Additionally, we prove that L-n is not a Lu Qi-Keng domain for n >= 3.
Název v anglickém jazyce
2-proper Holomorphic Images of Classical Cartan Domains
Popis výsledku anglicky
Motivated by the way two special domains, namely the symmetrized bidisc and the tetrablock, could be defined as the images of 2-proper holomorphic images of classical Car-tan domains, we present a general approach to study 2-proper holomorphic images of bounded symmetric domains. We show some special properties of 2-proper holomorphic maps (such as the construction of some involutive automorphisms, etc.) and enlist possible domains (up to biholomorphisms) which arise as 2-proper holomorphic images of bounded symmetric domains. This leads us to a consideration of a new family of domains Ln for n >= 2. Let Ln be an irreducible classical Cartan domain of type IV (Lie ball) of dimension n, and Lambda(n) : L-n -> Lambda(n)(L-n) := L(n )be the natural proper holomorphic mapping of multiplicity 2. It turns out that L-2 and L-3 are biholomorphic to the symmetrized bidisc and the tetrablock, respectively. In this article, we study function geometric properties of the family {L-n : n >= 2} in a unified manner, and thus extend results of many earlier papers on analogous properties of the symmetrized bidisc and the tetrablock. We show that L-n cannot be exhausted by domains biholomorhic to some convex domains. Any proper holomorphic self-mapping of L-n is an automorphism for n >= 3. Moreover, the automorphism group Aut(L-n) is isomorphic to Aut(Ln-1), and L-n is inhomogeneous for n >= 2. Additionally, we prove that L-n is not a Lu Qi-Keng domain for n >= 3.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
Projekt
<a href="/cs/project/GA21-27941S" target="_blank" >GA21-27941S: Teorie funkcí a příbuzné operátory na komplexních oblastech</a><br>
Návaznosti
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Ostatní
Rok uplatnění
2025
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Indiana University Mathematics Journal
ISSN
0022-2518
e-ISSN
1943-5258
Svazek periodika
74
Číslo periodika v rámci svazku
3
Stát vydavatele periodika
US - Spojené státy americké
Počet stran výsledku
29
Strana od-do
575-603
Kód UT WoS článku
001609258700002
EID výsledku v databázi Scopus
2-s2.0-105014733009