Abstract
We study spaces of ultradifferentiable functions which contain Gevrey classes. Although the corresponding defining sequences do not satisfy Komatsu’s condition (M.2)’, we prove appropriate continuity properties under the action of (ultra)differentiable operators. Furthermore, we study convenient localization procedure which leads to the concept of wave-front set with respect to our regularity conditions. As an application, we identify singular supports of suitable spaces of ultradifferentiable functions as standard projections of intersections/unions of wave-front sets.
Dedicated to Professor Pilipović on the occasion of his 65th birthday.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Teofanov, N., Tomić, F. (2017). Ultradifferentiable Functions of Class \( M_p^{\tau ,\sigma } \) and Microlocal Regularity. In: Oberguggenberger, M., Toft, J., Vindas, J., Wahlberg, P. (eds) Generalized Functions and Fourier Analysis. Operator Theory: Advances and Applications(), vol 260. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-51911-1_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-51911-1_12
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-51910-4
Online ISBN: 978-3-319-51911-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)