Loughborough University
Browse

File(s) under permanent embargo

Reason: This item is currently closed access.

Generalized Fourier integral operators on spaces of Colombeau type

chapter
posted on 2015-04-17, 13:49 authored 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

Usage metrics

    Loughborough Publications

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC