Almost analytic extensions of ultradifferentiable functions with applications to microlocal analysis
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F20%3A00114510" target="_blank" >RIV/00216224:14310/20:00114510 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jmaa.2019.123451" target="_blank" >https://doi.org/10.1016/j.jmaa.2019.123451</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2019.123451" target="_blank" >10.1016/j.jmaa.2019.123451</a>
Alternative languages
Result language
angličtina
Original language name
Almost analytic extensions of ultradifferentiable functions with applications to microlocal analysis
Original language description
We review and extend the description of ultradifferentiable functions by their almost analytic extensions, i.e., extensions to the complex domain with specific vanishing rate of the (partial derivative) over bar -derivative near the real domain. We work in a general uniform framework which comprises the main classical ultradifferentiable classes but also allows to treat unions and intersections of such. The second part of the paper is devoted to applications in microlocal analysis. The ultradifferentiable wave front set is defined in this general setting and characterized in terms of almost analytic extensions and of the FBI transform. This allows to extend its definition to ultradifferentiable manifolds. We also discuss ultradifferentiable versions of the elliptic regularity theorem and obtain a general quasianalytic Holmgren uniqueness theorem. (C) 2019 Elsevier Inc. All rights reserved.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA17-19437S" target="_blank" >GA17-19437S: Classification problems for real hypersurfaces in complex space</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Mathematical Analysis and Applications
ISSN
0022-247X
e-ISSN
1096-0813
Volume of the periodical
481
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
51
Pages from-to
1-51
UT code for WoS article
000488889600001
EID of the result in the Scopus database
2-s2.0-85071955077