A class of fourier integral operators on manifolds with boundary

Ubertino Battisti; Sandro Coriasco; Elmar Schrohe

doi:10.1007/978-3-319-14618-8_1

Details

Original language	English
Title of host publication	Pseudo-Differential Operators and Generalized Functions
Number of pages	19
ISBN (electronic)	978-3-319-14618-8
Publication status	Published - 2015

Publication series

Name	Operator Theory: Advances and Applications
Volume	245
ISSN (Print)	0255-0156

Abstract

We study a class of Fourier integral operators on compact manifolds with boundary X and Y, associated with a natural class of symplectomor-phisms χ: T^∗Y \0 → T^∗X \0, namely, those which preserve the boundary. A calculus of Boutet de Monvel’s type can be defined for such Fourier integral operators, and appropriate continuity properties established. One of the key features of this calculus is that the local representations of these operators are given by operator-valued symbols acting on Schwartz functions or temperate distributions. Here we focus on properties of the corresponding local phase functions, which allow to prove this result in a rather straightforward way.

Keywords

Boundary-pre-serving symplectomorphism, Fourier integral operator, Manifold with boundary

ASJC Scopus subject areas

Mathematics(all)
Analysis

Cite this

A class of fourier integral operators on manifolds with boundary. / Battisti, Ubertino; Coriasco, Sandro; Schrohe, Elmar.
Pseudo-Differential Operators and Generalized Functions. 2015. (Operator Theory: Advances and Applications; Vol. 245).

Research output: Chapter in book/report/conference proceeding › Contribution to book/anthology › Research › peer review

Battisti, U, Coriasco, S & Schrohe, E 2015, A class of fourier integral operators on manifolds with boundary. in Pseudo-Differential Operators and Generalized Functions. Operator Theory: Advances and Applications, vol. 245. https://doi.org/10.1007/978-3-319-14618-8_1

Battisti, U., Coriasco, S., & Schrohe, E. (2015). A class of fourier integral operators on manifolds with boundary. In Pseudo-Differential Operators and Generalized Functions (Operator Theory: Advances and Applications; Vol. 245). https://doi.org/10.1007/978-3-319-14618-8_1

Battisti U, Coriasco S, Schrohe E. A class of fourier integral operators on manifolds with boundary. In Pseudo-Differential Operators and Generalized Functions. 2015. (Operator Theory: Advances and Applications). doi: 10.1007/978-3-319-14618-8_1

Battisti, Ubertino ; Coriasco, Sandro ; Schrohe, Elmar. / A class of fourier integral operators on manifolds with boundary. Pseudo-Differential Operators and Generalized Functions. 2015. (Operator Theory: Advances and Applications).

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Research@Leibniz University

A class of fourier integral operators on manifolds with boundary

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