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 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 . We also develop the corresponding symbolic calculus.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm167-2-1,
author = {C. Fern\'andez and A. Galbis and D. Jornet},
title = {Pseudodifferential operators on non-quasianalytic classes of Beurling type},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {99-131},
zbl = {1075.46033},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm167-2-1}
}
C. Fernández; A. Galbis; D. Jornet. Pseudodifferential operators on non-quasianalytic classes of Beurling type. Studia Mathematica, Tome 166 (2005) pp. 99-131. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm167-2-1/