Bounded spherical functions and Heisenberg inequality on quaternionic Heisenberg group

被引：0

作者：

Amghar, Walid ^{[1
]}

Fahlaoui, Said ^{[1
]}

机构：

[1] Univ Moulay Ismail, Dept Math, Fac Sci, BP 11201, Zitoune, Meknes, Morocco

来源：

ADVANCES IN OPERATOR THEORY | 2022年 / 7卷 / 02期

关键词：

Quaternionic Heisenberg group; Spherical functions; Spherical Gabor transform; Heisenberg inequality;

D O I：

10.1007/s43036-022-00188-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we will construct the bounded spherical functions of the quaternionic Heisenberg group using the theory of representations of the semi-direct product of H-q and the subgroup K of the quaternions of module 1. Finally, we prove the Heisenberg inequality for the spherical Fourier transform and the spherical Gabor transform on the Quaternionic Heisenberg group.

引用

页数：19

共 50 条

[1] Bounded spherical functions and Heisenberg inequality on quaternionic Heisenberg group
Walid Amghar
Said Fahlaoui
[J]. Advances in Operator Theory, 2022, 7
[2] Spherical Fourier transform on the quaternionic Heisenberg group
Faress, Moussa
Fahlaoui, Said
[J]. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2020, 31 (09) : 685 - 701
[3] ON THE QUATERNIONIC HEISENBERG-GROUP
CORDERO, LA
FERNANDEZ, M
DELEON, M
[J]. BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 1987, 1A (01): : 31 - 37
[4] BOUNDED K-SPHERICAL FUNCTIONS ON HEISENBERG GROUPS
BENSON, C
JENKINS, J
RATCLIFF, G
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1992, 105 (02) : 409 - 443
[5] Spaces of bounded spherical functions on Heisenberg groups: part II
Chal Benson
Gail Ratcliff
[J]. Annali di Matematica Pura ed Applicata (1923 -), 2015, 194 : 533 - 561
[6] Spaces of bounded spherical functions on Heisenberg groups: part II
Benson, Chal
Ratcliff, Gail
[J]. ANNALI DI MATEMATICA PURA ED APPLICATA, 2015, 194 (02) : 533 - 561
[7] Conjugate points on the quaternionic Heisenberg group
Jang, C
Kim, J
Kim, Y
Park, K
[J]. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2003, 40 (01) : 61 - 72
[8] The quaternionic Monge–Ampère operator and plurisubharmonic functions on the Heisenberg group
Wei Wang
[J]. Mathematische Zeitschrift, 2021, 298 : 521 - 549
[9] Asymptotics for certain harmonic functions and the Martin compactification on the quaternionic Heisenberg group
Luan, JW
Zhu, FL
[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2005, 21 (06) : 1295 - 1308
[10] The quaternionic Monge-Ampere operator and plurisubharmonic functions on the Heisenberg group
Wang, Wei
[J]. MATHEMATISCHE ZEITSCHRIFT, 2021, 298 (1-2) : 521 - 549

← 1 2 3 4 5 →