Reproducing kernels for holomorphic functions on some balls related to the Lie ball

Keiko Fujita. "Reproducing kernels for holomorphic functions on some balls related to the Lie ball." Annales Polonici Mathematici 91.2-3 (2007): 219-234. <http://eudml.org/doc/280380>.

@article{KeikoFujita2007,
abstract = {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.},
author = {Keiko Fujita},
journal = {Annales Polonici Mathematici},
keywords = {Lie balls; holomorphic and harmonic extensions; integral representation; reproducing kernel; Bergman kernel; Szegő kernels},
language = {eng},
number = {2-3},
pages = {219-234},
title = {Reproducing kernels for holomorphic functions on some balls related to the Lie ball},
url = {http://eudml.org/doc/280380},
volume = {91},
year = {2007},
}

TY - JOUR
AU - Keiko Fujita
TI - Reproducing kernels for holomorphic functions on some balls related to the Lie ball
JO - Annales Polonici Mathematici
PY - 2007
VL - 91
IS - 2-3
SP - 219
EP - 234
AB - 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.
LA - eng
KW - Lie balls; holomorphic and harmonic extensions; integral representation; reproducing kernel; Bergman kernel; Szegő kernels
UR - http://eudml.org/doc/280380
ER -