We generalize to the case of several variables the classical theorems on the holomorphic extension of the Cauchy transforms. The Cauchy transformation is considered in the setting of tempered distributions and the Cauchy kernel is modified to a rapidly decreasing function. The results are applied to the study of "continuous" Taylor expansions and to singular partial differential equations.
@article{bwmeta1.element.bwnjournal-article-smv102i1p1bwm,
author = {Bogdan Ziemian},
title = {The modified Cauchy transformation with applications to generalized Taylor expansions},
journal = {Studia Mathematica},
volume = {103},
year = {1992},
pages = {1-24},
zbl = {0815.46035},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv102i1p1bwm}
}
Ziemian, Bogdan. The modified Cauchy transformation with applications to generalized Taylor expansions. Studia Mathematica, Tome 103 (1992) pp. 1-24. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv102i1p1bwm/
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