Regularization of norms of Lagrangian distributions

Author:
Steven Izen

Journal:
Trans. Amer. Math. Soc. **288** (1985), 363-380

MSC:
Primary 58G15

DOI:
https://doi.org/10.1090/S0002-9947-1985-0773065-1

MathSciNet review:
773065

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Abstract: Let be a compact smooth manifold, . Let be a fixed Lagrangian submanifold of . The space of Lagrangian distributions is contained in if . When , just misses . A new inner product is defined on in terms of symbols. This inner product contains " information" in the following sense: Slight regularizations of the Lagrangian distributions are taken, putting them in . The asymptotic behavior of the inner product is examined as the regularizations approach the identity. Three different regularization schemes are presented and, in each case, is found to regulate the growth of the ordinary inner product.

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DOI:
https://doi.org/10.1090/S0002-9947-1985-0773065-1

Article copyright:
© Copyright 1985
American Mathematical Society