We consider holomorphic functions and complex harmonic functions on some balls, including the complex Euclidean ball, the Lie ball and the dual Lie ball. After reviewing some results on Bergman kernels and harmonic Bergman kernels for these balls, we consider harmonic continuation of complex harmonic functions on these balls by using harmonic Bergman kernels. We also study Szegő kernels and harmonic Szegő kernels for these balls.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap91-2-9,
author = {Keiko Fujita},
title = {Reproducing kernels for holomorphic functions on some balls related to the Lie ball},
journal = {Annales Polonici Mathematici},
volume = {92},
year = {2007},
pages = {219-234},
zbl = {1153.32005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap91-2-9}
}
Keiko Fujita. Reproducing kernels for holomorphic functions on some balls related to the Lie ball. Annales Polonici Mathematici, Tome 92 (2007) pp. 219-234. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap91-2-9/