We study isometries between spaces of weighted holomorphic functions. We show that such isometries have a canonical form determined by a group of homeomorphisms of a distinguished subset of the range and domain. A number of invariants for these isometries are determined. For specific families of weights we classify the form isometries can take.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm190-3-1,
author = {Christopher Boyd and Pilar Rueda},
title = {Isometries between spaces of weighted holomorphic functions},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {203-231},
zbl = {1172.46005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm190-3-1}
}
Christopher Boyd; Pilar Rueda. Isometries between spaces of weighted holomorphic functions. Studia Mathematica, Tome 192 (2009) pp. 203-231. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm190-3-1/