Quaternion H-type group and differential operator Δλ

被引：13

作者：

Chang Der-Chen ^{[1
]}

Markina, Irina ^{[2
]}

机构：

[1] Georgetown Univ, Dept Math, Washington, DC 20057 USA

[2] Univ Bergen, Dept Math, N-5008 Bergen, Norway

来源：

SCIENCE IN CHINA SERIES A-MATHEMATICS | 2008年 / 51卷 / 04期

关键词：

quaternion; Siegel half space; q-holomorphic function; subelliptic operator;

D O I：

10.1007/s11425-007-0133-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the relations between the quaternion H-type group and the boundary of the unit ball on the two-dimensional quaternionic space. The orthogonal projection of the space of square integrable functions defined on quaternion H-type group into its subspace of boundary values of q-holomorphic functions is considered. The precise form of Cauchy-Szego kernel and the orthogonal projection operator is obtained. The fundamental solution for the operator Delta(lambda) is found.

引用

页码：523 / 540

页数：18

共 20 条

[1]

Adams WW., 1999, J GEOM ANAL, V9, P1, DOI [DOI 10.1007/BF02923085.MR1760717, 10.1007/BF02923085, DOI 10.1007/BF02923085]

[2]

CALIN O, 2005, IN PRESS AMS IP SERI

[3]

CALIN O, 2005, HARMONIC ANAL SIGNAL

[4] Geometric analysis on quaternion H-type groups [J].

Chang, DC ;

Markina, I .

JOURNAL OF GEOMETRIC ANALYSIS, 2006, 16 (02) :265-294

[5] H-TYPE GROUPS AND IWASAWA DECOMPOSITIONS [J].

COWLING, M ;

DOOLEY, AH ;

KORANYI, A ;

RICCI, F .

ADVANCES IN MATHEMATICS, 1991, 87 (01) :1-41

[6] QUATERNION CALCULUS [J].

DEAVOURS, CA .

AMERICAN MATHEMATICAL MONTHLY, 1973, 80 (09) :995-1008

[7]

Folland G.B., 1982, MATH NOTES, V28, pxii+285

[8] FUNDAMENTAL SOLUTION FOR A SUBELLIPTIC OPERATOR [J].

FOLLAND, GB .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 79 (02) :373-376

[9]

Fueter R., 1934, Comment. Math. Helv., V7, P307, DOI [10.1007/BF01292723, 10.1007/BF01292723), DOI 10.1007/BF01292723]

[10]

Fueter R., 1936, Comment. Math. Helv, V8, P371, DOI [10.1007/BF01199562, DOI 10.1007/BF01199562]

← 1 2 →