文摘
We define and study classes of smooth functions which are less regular than Gevrey functions. To that end we introduce two-parameter dependent sequences which do not satisfy Komatsu’s condition (M.2)’, which implies stability under differential operators within the spaces of ultradifferentiable functions. Our classes therefore have particular behavior under the action of differentiable operators. On a more advanced level, we study microlocal properties and prove that $$\begin{aligned} {\text {WF}}_{0,\infty }(P(D)u)\subseteq {\text {WF}}_{0,\infty }(u)\subseteq {\text {WF}}_{0,\infty }(P(D)u) \cup \mathrm{Char}(P), \end{aligned}$$where u is a Schwartz distribution, P(D) is a partial differential operator with constant coefficients and \({\text {WF}}_{0,\infty }\) is the wave front set described in terms of new regularity conditions. For the analysis we introduce particular admissibility condition for sequences of cut-off functions, and a new technical tool called enumeration. Keywords Ultradifferentiable functions Gevrey classes Ultradistributions Wave-front sets Mathematics Subject Classification Primary 35A18 46F05 Secondary 46F10 Page %P Close Plain text Look Inside Reference tools Export citation EndNote (.ENW) JabRef (.BIB) Mendeley (.BIB) Papers (.RIS) Zotero (.RIS) BibTeX (.BIB) Add to Papers Other actions Register for Journal Updates About This Journal Reprints and Permissions Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn Related Content Supplementary Material (0) References (32) References1.Cappiello, M., Schulz, R.: Microlocal analysis of quasianalytic Gelfand-Shilov type ultradistributions, preprint versoin arXiv:1309.4236v1 [math.AP]. 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(2015). doi:10.1007/s11868-015-0143-7 32.Wahlberg, P.: Propagation of polynomial phase space singularities for Schrdinger equations with quadratic Hamiltonians (2015). arXiv:1411.6518v3 [math.AP] About this Article Title Beyond Gevrey regularity Journal Journal of Pseudo-Differential Operators and Applications Volume 7, Issue 1 , pp 113-140 Cover Date2016-03 DOI 10.1007/s11868-016-0145-0 Print ISSN 1662-9981 Online ISSN 1662-999X Publisher Springer International Publishing Additional Links Register for Journal Updates Editorial Board About This Journal Manuscript Submission Topics Analysis Operator Theory Partial Differential Equations Functional Analysis Applications of Mathematics Algebra Keywords Ultradifferentiable functions Gevrey classes Ultradistributions Wave-front sets Primary 35A18 46F05 Secondary 46F10 Authors Stevan Pilipović (1) Nenad Teofanov (1) Filip Tomić (2) Author Affiliations 1. Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Novi Sad, Serbia 2. Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia Continue reading... To view the rest of this content please follow the download PDF link above.