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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

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Microlocal analysis of some isospectral deformations
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by F. Marhuenda
Trans. Amer. Math. Soc. 343 (1994), 245-275
DOI: https://doi.org/10.1090/S0002-9947-1994-1181185-0
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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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Bibliographic Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 343 (1994), 245-275
  • MSC: Primary 58G15; Secondary 35S30, 58G25
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1181185-0
  • MathSciNet review: 1181185