Ultraregular generalized functions of Colombeau type

J. Math. Sci. Univ. Tokyo
Vol. 15 (2008), No. 4, Page 427--447.

Ultraregular generalized functions of Colombeau type
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General algebras of ultradifferentiable generalized functions satisfying some regularity assumptions are introduced. We give a microlocal analysis within these algebras related to the regularity type and the ultradifferentiable property. As a particular case we obtain new algebras of Gevrey generalized functions.

Keywords: Generalized functions, ultradifferentiable functions, Colombeau algebra, wave front, microlocal analysis, Denjoy-Carleman classes, Gevrey generalized functions

Mathematics Subject Classification (2000): Primary 46F30, secondary 35A18, 46F10
Mathematical Reviews Number: MR2546904

Received: 2007-05-10