Bases in spaces of analytic germs

Michael Langenbruch. "Bases in spaces of analytic germs." Annales Polonici Mathematici 106.1 (2012): 223-243. <http://eudml.org/doc/286178>.

@article{MichaelLangenbruch2012,
abstract = {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 $S¹_\{α\}$ and $S₁^\{α\}$ for α > 0 and to the spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions.},
author = {Michael Langenbruch},
journal = {Annales Polonici Mathematici},
keywords = {bases; analytic germs; power series space; tame mapping; linear topological invariant; property (DN); property ; Gelfand-Shilov spaces; Fourier hyperfunctions; modified Fourier hyperfunctions},
language = {eng},
number = {1},
pages = {223-243},
title = {Bases in spaces of analytic germs},
url = {http://eudml.org/doc/286178},
volume = {106},
year = {2012},
}

TY - JOUR
AU - Michael Langenbruch
TI - Bases in spaces of analytic germs
JO - Annales Polonici Mathematici
PY - 2012
VL - 106
IS - 1
SP - 223
EP - 243
AB - 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 $S¹_{α}$ and $S₁^{α}$ for α > 0 and to the spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions.
LA - eng
KW - bases; analytic germs; power series space; tame mapping; linear topological invariant; property (DN); property ; Gelfand-Shilov spaces; Fourier hyperfunctions; modified Fourier hyperfunctions
UR - http://eudml.org/doc/286178
ER -