Approximation properties of local smoothing kernels

Abstract

We study some properties of smoothing kernels and their local expression as they appear in the construction of Colombeau-type generalized function algebras that are diffeomorphism-invariant.

Keywords:

• smoothing kernels
• convolution
• Colombeau algebra

AMS Subject Classification :

• 44A35
• 46F30

Acknowledgements

This research has been supported by START-project Y237 and project P20525 of the Austrian Science Fund and the Doctoral College ‘Differential Geometry and Lie Groups’ of the University of Vienna.