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- W2020175181 abstract "Let $X$ be a compact smooth manifold, $dim X = n$. Let $Lambda$ be a fixed Lagrangian submanifold of ${T^ast }X$. The space of Lagrangian distributions ${I^k}(X,Lambda )$ is contained in ${L^2}(X)$ if $k < - n/4$. When $k = n/4$, ${I^{ - n/4}}(X,Lambda )$ just misses ${L^2}(X)$. A new inner product ${langle u,vrangle _R}$ is defined on ${I^{ - n/4}}(X,Lambda )/{I^{ - n/4 - 1}}(X,Lambda )$ in terms of symbols. This inner product contains ${L^2}$ information in the following sense: Slight regularizations of the Lagrangian distributions are taken, putting them in ${L^2}(X)$. The asymptotic behavior of the ${L^2}$ inner product is examined as the regularizations approach the identity. Three different regularization schemes are presented and, in each case, ${langle u,vrangle _R}$ is found to regulate the growth of the ordinary ${L^2}$ inner product." @default.
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- W2020175181 date "1985-01-01" @default.
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- W2020175181 title "Regularization of $Lsp 2$ norms of Lagrangian distributions" @default.
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- W2020175181 doi "https://doi.org/10.1090/s0002-9947-1985-0773065-1" @default.
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