Polynomial null solutions to bosonic Laplacians, bosonic bergman and hardy spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F22%3A00129420" target="_blank" >RIV/00216224:14310/22:00129420 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1017/S0013091522000426" target="_blank" >https://doi.org/10.1017/S0013091522000426</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/S0013091522000426" target="_blank" >10.1017/S0013091522000426</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Polynomial null solutions to bosonic Laplacians, bosonic bergman and hardy spaces

Popis výsledku v původním jazyce

A bosonic Laplacian, which is a generalization of Laplacian, is constructed as a second-order conformally invariant differential operator acting on functions taking values in irreducible representations of the special orthogonal group, hence of the spin group. In this paper, we firstly introduce some properties for homogeneous polynomial null solutions to bosonic Laplacians, which give us some important results, such as an orthogonal decomposition of the space of polynomials in terms of homogeneous polynomial null solutions to bosonic Laplacians, etc. This work helps us to introduce Bergman spaces related to bosonic Laplacians, named as bosonic Bergman spaces, in higher spin spaces. Reproducing kernels for bosonic Bergman spaces in the unit ball and a description of bosonic Bergman projection are given as well. At the end, we investigate bosonic Hardy spaces, which are considered as generalizations of harmonic Hardy spaces. Analogs of some well-known results for harmonic Hardy spaces are provided here. For instance, connections to certain complex Borel measure spaces, growth estimates for functions in the bosonic Hardy spaces, etc.

Název v anglickém jazyce

Polynomial null solutions to bosonic Laplacians, bosonic bergman and hardy spaces

Popis výsledku anglicky

A bosonic Laplacian, which is a generalization of Laplacian, is constructed as a second-order conformally invariant differential operator acting on functions taking values in irreducible representations of the special orthogonal group, hence of the spin group. In this paper, we firstly introduce some properties for homogeneous polynomial null solutions to bosonic Laplacians, which give us some important results, such as an orthogonal decomposition of the space of polynomials in terms of homogeneous polynomial null solutions to bosonic Laplacians, etc. This work helps us to introduce Bergman spaces related to bosonic Laplacians, named as bosonic Bergman spaces, in higher spin spaces. Reproducing kernels for bosonic Bergman spaces in the unit ball and a description of bosonic Bergman projection are given as well. At the end, we investigate bosonic Hardy spaces, which are considered as generalizations of harmonic Hardy spaces. Analogs of some well-known results for harmonic Hardy spaces are provided here. For instance, connections to certain complex Borel measure spaces, growth estimates for functions in the bosonic Hardy spaces, etc.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ19-14413Y" target="_blank" >GJ19-14413Y: Lineární a nelineární eliptické rovnice se singulárními daty a související problémy</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Proceedings of the Edinburgh Mathematical Society

ISSN

0013-0915

e-ISSN

1464-3839

Svazek periodika

65

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

32

Strana od-do

958-989

Kód UT WoS článku

000867457500001

EID výsledku v databázi Scopus

2-s2.0-85147498431