Pseudodifferential operators on non-quasianalytic classes of Beurling type

C. Fernández, A. Galbis, and D. Jornet. "Pseudodifferential operators on non-quasianalytic classes of Beurling type." Studia Mathematica 167.2 (2005): 99-131. <http://eudml.org/doc/284882>.

@article{C2005,
abstract = {We introduce pseudodifferential operators (of infinite order) in the framework of non-quasianalytic classes of Beurling type. We prove that such an operator with (distributional) kernel in a given Beurling class $ ^\{\prime \}_\{(ω)\}$ is pseudo-local and can be locally decomposed, modulo a smoothing operator, as the composition of a pseudodifferential operator of finite order and an ultradifferential operator with constant coefficients in the sense of Komatsu, both operators with kernel in the same class $ ^\{\prime \}_\{(ω)\}$. We also develop the corresponding symbolic calculus.},
author = {C. Fernández, A. Galbis, D. Jornet},
journal = {Studia Mathematica},
keywords = {pseudodifferential operator; ultradistribution; non-quasianalytic},
language = {eng},
number = {2},
pages = {99-131},
title = {Pseudodifferential operators on non-quasianalytic classes of Beurling type},
url = {http://eudml.org/doc/284882},
volume = {167},
year = {2005},
}

TY - JOUR
AU - C. Fernández
AU - A. Galbis
AU - D. Jornet
TI - Pseudodifferential operators on non-quasianalytic classes of Beurling type
JO - Studia Mathematica
PY - 2005
VL - 167
IS - 2
SP - 99
EP - 131
AB - We introduce pseudodifferential operators (of infinite order) in the framework of non-quasianalytic classes of Beurling type. We prove that such an operator with (distributional) kernel in a given Beurling class $ ^{\prime }_{(ω)}$ is pseudo-local and can be locally decomposed, modulo a smoothing operator, as the composition of a pseudodifferential operator of finite order and an ultradifferential operator with constant coefficients in the sense of Komatsu, both operators with kernel in the same class $ ^{\prime }_{(ω)}$. We also develop the corresponding symbolic calculus.
LA - eng
KW - pseudodifferential operator; ultradistribution; non-quasianalytic
UR - http://eudml.org/doc/284882
ER -