Abstract
We study integration and Fourier transform in the Colombeau algebra Gτ of tempered generalized functions using a general damping factor. This unifies different settings described earlier by J. F. Colombeau, M. Nedeljikov, S. Pilipović, and M. Damsma (for a simplified version). Further we prove characterizations of regularity for generalized functions in two situations: compactly supported or in the image of S′ inside Gτ. Finally we investigate the notion of wave front set in the Colombeau algebra G(Ω), Ω an open subset of Rn, and show that it is in fact independent of the damping measure used for Fourier transform.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
