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

J 2022

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

DING, Chao; Phuoc Tai NGUYEN a Ryan JOHN

Základní údaje

Originální název

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

Autoři

DING, Chao; Phuoc Tai NGUYEN a Ryan JOHN

Vydání

Proceedings of the Edinburgh Mathematical Society, Cambridge University Press, 2022, 0013-0915

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.700

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/22:00129420

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

Bosonic Laplacians; real analyticity; L-2 decomposition; bosonic Hardy spaces; bosonic Bergman spaces

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 28. 2. 2023 16:17, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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.

Návaznosti

GJ19-14413Y, projekt VaV

Název: Lineární a nelineární eliptické rovnice se singulárními daty a související problémy

Investor: Grantová agentura ČR, Lineární a nelineární eliptické rovnice se singulárními daty a související problémy

Citovat

DING, Chao; Phuoc Tai NGUYEN a Ryan JOHN. Polynomial null solutions to bosonic Laplacians, bosonic bergman and hardy spaces. Proceedings of the Edinburgh Mathematical Society. Cambridge University Press, 2022, roč. 65, č. 4, s. 958-989. ISSN 0013-0915. Dostupné z: https://doi.org/10.1017/S0013091522000426.

@article{2262457,
   author = {Ding, Chao and Nguyen, Phuoc Tai and John, Ryan},
   article_number = {4},
   doi = {https://doi.org/10.1017/S0013091522000426},
   keywords = {Bosonic Laplacians; real analyticity; L-2 decomposition; bosonic Hardy spaces; bosonic Bergman spaces},
   language = {eng},
   issn = {0013-0915},
   journal = {Proceedings of the Edinburgh Mathematical Society},
   title = {Polynomial null solutions to bosonic Laplacians, bosonic bergman and hardy spaces},
   url = {https://doi.org/10.1017/S0013091522000426},
   volume = {65},
   year = {2022}
}

TY  - JOUR
ID  - 2262457
AU  - Ding, Chao - Nguyen, Phuoc Tai - John, Ryan
PY  - 2022
TI  - Polynomial null solutions to bosonic Laplacians, bosonic bergman and hardy spaces
JF  - Proceedings of the Edinburgh Mathematical Society
VL  - 65
IS  - 4
SP  - 958-989
EP  - 958-989
PB  - Cambridge University Press
SN  - 00130915
KW  - Bosonic Laplacians
KW  - real analyticity
KW  - L-2 decomposition
KW  - bosonic Hardy spaces
KW  - bosonic Bergman spaces
UR  - https://doi.org/10.1017/S0013091522000426
N2  - 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.
ER  -

DING, Chao; Phuoc Tai NGUYEN a Ryan JOHN. Polynomial null solutions to bosonic Laplacians, bosonic bergman and hardy spaces. \textit{Proceedings of the Edinburgh Mathematical Society}. Cambridge University Press, 2022, roč.~65, č.~4, s.~958-989. ISSN~0013-0915. Dostupné z: https://doi.org/10.1017/S0013091522000426.

Přehled o publikaci