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Metadata --- Digital Assets --- Embedding

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Ordered algebraic structures --- Algebra, Universal. --- Embedding theorems. --- Magic squares. --- Quasigroups.

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Breast Neoplasms --- Receptors, Estrogen --- Paraffin Embedding --- therapy --- analysis

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Let X be an abstract not necessarily compact orientable CR manifold of dimension 2n-1, ngeqslant 2, and let L^k be the k-th tensor power of a CR complex line bundle L over X. Given qin {0,1,ldots ,n-1}, let Box ^{(q)}_{b,k} be the Gaffney extension of Kohn Laplacian for (0,q) forms with values in L^k. For lambda geq 0, let Pi ^{(q)}_{k,leq lambda} :=E((-infty ,lambda ]), where E denotes the spectral measure of Box ^{(q)}_{b,k}. In this work, the author proves that Pi ^{(q)}_{k,leq k^{-N_0}}F^*_k, F_kPi ^{(q)}_{k,leq k^{-N_0}}F^*_k, N_0geq 1, admit asymptotic expansions with respect to k on the non-degenerate part of the characteristic manifold of Box ^{(q)}_{b,k}, where F_k is some kind of microlocal cut-off function. Moreover, we show that F_kPi ^{(q)}_{k,leq 0}F^*_k admits a full asymptotic expansion with respect to k if Box ^{(q)}_{b,k} has small spectral gap property with respect to F_k and Pi^{(q)}_{k,leq 0} is k-negligible away the diagonal with respect to F_k. By using these asymptotics, the authors establish almost Kodaira embedding theorems on CR manifolds and Kodaira embedding theorems on CR manifolds with transversal CR S^1 action.

Embedding theorems. --- CR submanifolds. --- Manifolds (Mathematics) --- Embeddings (Mathematics) --- Kernel functions. --- Asymptotic expansions.

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517.982 --- 517.982 Linear spaces with topology and order or other structures --- Linear spaces with topology and order or other structures --- Integral representations --- Representations, Integral --- Imbedding theorems --- Theorems, Embedding --- Theorems, Imbedding --- Embeddings (Mathematics) --- Functions of several real variables. --- Invariant embedding. --- Functions of several real variables --- Lebesgue integration --- Invariant imbedding --- Invariant imbedding. --- Embedding theorems --- Functions of several complex variables --- Algebraic number theory --- Crystallography, Mathematical --- Representations of groups --- Complex variables --- Several complex variables, Functions of --- Functions of complex variables --- Functional analysis --- Invariant embedding