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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Microlocal analysis of some isospectral deformations


Author: F. Marhuenda
Journal: Trans. Amer. Math. Soc. 343 (1994), 245-275
MSC: Primary 58G15; Secondary 35S30, 58G25
MathSciNet review: 1181185
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Abstract: We study the microlocal structure of the examples of isospectral deformations of Riemannian manifolds given by D. DeTurck and C. Gordon in [DeT-Gl]. The Schwartz kernel of the intertwining operators considered by them may be written as an oscillatory integral with a singular phase function and product type amplitude. In certain instances, we identify them as belonging to the space of Fourier integral operators associated with various pairwise intersecting Lagrangians. After formulating a class of operators incorporating the most relevant features of the operators above, we establish a composition calculus for this class and show that is not necessary to introduce new Lagrangians in the composition.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1181185-0
PII: S 0002-9947(1994)1181185-0
Article copyright: © Copyright 1994 American Mathematical Society