We prove precise decomposition results and logarithmically convex estimates in certain weighted spaces of holomorphic germs near ℝ. These imply that the spaces have a basis and are tamely isomorphic to the dual of a power series space of finite type which can be calculated in many situations. Our results apply to the Gelfand-Shilov spaces and for α > 0 and to the spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap106-0-18,
author = {Michael Langenbruch},
title = {Bases in spaces of analytic germs},
journal = {Annales Polonici Mathematici},
volume = {105},
year = {2012},
pages = {223-243},
zbl = {1267.46038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap106-0-18}
}
Michael Langenbruch. Bases in spaces of analytic germs. Annales Polonici Mathematici, Tome 105 (2012) pp. 223-243. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap106-0-18/