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.
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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
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DOI: https://doi.org/10.1007/978-3-319-51911-1_12
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-51910-4
Online ISBN: 978-3-319-51911-1
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