Open AccessBeyond gevrey regularity: Superposition and propagation of singularities
Author(s) -
Stevan Pilipović,
Nenad Teofanov,
Filip Tomić
Publication year - 2018
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1808763p
Subject(s) - mathematics , superposition principle , gravitational singularity , relaxation (psychology) , mathematical analysis , space (punctuation) , sequence (biology) , inverse , type (biology) , pure mathematics , partial differential equation , partial derivative , geometry , psychology , social psychology , linguistics , philosophy , ecology , biology , genetics
We propose the relaxation of Gevrey regularity condition by using sequences which depend on two parameters, and define spaces of ultradifferentiable functions which contain Gevrey classes. It is shown that such a space is closed under superposition, and therefore inverse closed as well. Furthermore, we study partial differential operators whose coefficients are less regular then Gevrey-type ultradifferentiable functions. To that aim we introduce appropriate wave front sets and prove a theorem on propagation of singularities. This extends related known results in the sense that assumptions on the regularity of the coefficients are weakened.