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Generalized Fourier integral operators on spaces of Colombeau type

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posted on 17.04.2015, 13:49 by Claudia Garetto
Generalized Fourier integral operators (FIOs) acting on Colombeau algebras are defined. This is based on a theory of generalized oscillatory integrals (OIs) whose phase functions as well as amplitudes may be generalized functions of Colombeau type. The mapping properties of these FIOs are studied as the composition with a generalized pseudodifferential operator. Finally, the microlocal Colombeau regularity for OIs and the influence of the FIO action on generalized wave front sets are investigated. This theory of generalized FIOs is motivated by the need of a general framework for partial differential operators with non-smooth coefficients and distributional data.

Funding

This work was completed with the support of FWF (Austria), grants T305-N13 and Y237-N13.

History

School

  • Science

Department

  • Mathematical Sciences

Citation

GARETTO, C., 2008. Generalized Fourier integral operators on spaces of Colombeau type.IN: Rodino, L. and Wong, M.W. (eds). New Developments in Pseudo-Differential Operators. Basel: Birkhauser-Verlag, pp. 137-184.

Publisher

© Birkhauser Verlag

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2008

Notes

This book chapter is closed access.

ISBN

9783764389680

Book series

Operator Theory: Advances and Operations;189

Language

en

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