Weighted Bergman kernels for nearly holomorphic functions on bounded symmetric domains

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00579463" target="_blank" >RIV/67985840:_____/24:00579463 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/47813059:19610/24:A0000152

Výsledek na webu

<a href="https://doi.org/10.1016/j.jfa.2023.110213" target="_blank" >https://doi.org/10.1016/j.jfa.2023.110213</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jfa.2023.110213" target="_blank" >10.1016/j.jfa.2023.110213</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Weighted Bergman kernels for nearly holomorphic functions on bounded symmetric domains

Popis výsledku v původním jazyce

We identify the standard weighted Bergman kernels of spaces of nearly holomorphic functions, in the sense of Shimura, on bounded symmetric domains. This also yields a description of the analogous kernels for spaces of “invariantly-polyanalytic” functions — a generalization of the ordinary polyanalytic functions on the ball which seems to be the most appropriate one from the point of view of holomorphic invariance. In both cases, the kernels turn out to be given by certain spherical functions, or equivalently Heckman-Opdam hypergeometric functions, and a conjecture relating some of these to a Faraut-Koranyi hypergeometric function is formulated based on the study of low rank situations. Finally, analogous results are established also for compact Hermitian symmetric spaces, where explicit formulas in terms of multivariable Jacobi polynomials are given.

Název v anglickém jazyce

Weighted Bergman kernels for nearly holomorphic functions on bounded symmetric domains

Popis výsledku anglicky

We identify the standard weighted Bergman kernels of spaces of nearly holomorphic functions, in the sense of Shimura, on bounded symmetric domains. This also yields a description of the analogous kernels for spaces of “invariantly-polyanalytic” functions — a generalization of the ordinary polyanalytic functions on the ball which seems to be the most appropriate one from the point of view of holomorphic invariance. In both cases, the kernels turn out to be given by certain spherical functions, or equivalently Heckman-Opdam hypergeometric functions, and a conjecture relating some of these to a Faraut-Koranyi hypergeometric function is formulated based on the study of low rank situations. Finally, analogous results are established also for compact Hermitian symmetric spaces, where explicit formulas in terms of multivariable Jacobi polynomials are given.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA21-27941S" target="_blank" >GA21-27941S: Teorie funkcí a příbuzné operátory na komplexních oblastech</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Functional Analysis

ISSN

0022-1236

e-ISSN

1096-0783

Svazek periodika

286

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

47

Strana od-do

110213

Kód UT WoS článku

001109009500001

EID výsledku v databázi Scopus

2-s2.0-85175806248