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# Szegő kernel asymptotics for high power of CR line bundles and Kodaira embedding theorems on CR manifolds

Author: Chin-Yu Hsiao; American Mathematical Society, Providence, Rhode Island : American Mathematical Society, [2018] ©2018 Memoirs of the American Mathematical Society, no. 1217. eBook : Document : EnglishView all editions and formats Let X be an abstract not necessarily compact orientable CR manifold of dimension 2n-1, n\geqslant 2, and let L^k be the k-th tensor power of a CR complex line bundle L over X. Given q\in \{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_k\Pi ^{(q)}_{k,\leq k^{-N_0}}F^*_k, N_0\geq 1, admit asymptotic expansions with.  Read more... (not yet rated) 0 with reviews - Be the first.

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Genre/Form: Electronic books Print version:HSIAO, CHIN-YU.SZEGO KERNEL ASYMPTOTICS FOR HIGH POWER OF CR LINE BUNDLES AND KODAIRA EMBEDDING THEOREMS ON CR... MANIFOLDS.[S.l.] : AMER MATHEMATICAL SOCIETY, 2018(OCoLC)1031944776 Document, Internet resource Internet Resource, Computer File Chin-Yu Hsiao; American Mathematical Society, Find more information about: Chin-Yu Hsiao 9781470447502 1470447509 1039082787 "July 2018, volume 254, number 1217 (fifth of 5 numbers)" 1 online resource (v, 142 pages). Cover; Title page; Chapter 1. Introduction and statement of the main results; 1.1. Main results: Szegő kernel asymptotics for lower energy forms and almost Kodaira embedding Theorems on CR manifolds; 1.2. Main results: Szegő kernel asymptotics; 1.3. Main results: Szegő kernel asymptotics and Kodairan embedding theorems on CR manifolds with transversal CR ¹ actions; Chapter 2. More properties of the phase ( , , ); Chapter 3. Preliminaries; 3.1. Some standard notations; 3.2. Set up and Terminology 7.1. Asymptotic upper bounds7.2. Kernel of the spectral function; 7.3. Szegö kernel asymptotics for lower energy forms; Chapter 8. Almost Kodaira embedding Theorems on CR manifolds; Chapter 9. Asymptotic expansion of the Szegö kernel; Chapter 10. Szegő kernel asymptotics and Kodairan embedding theorems on CR manifolds with transversal CR ¹ actions; 10.1. CR manifolds in projective spaces; 10.2. Compact Heisenberg groups; 10.3. Holomorphic line bundles over a complex torus; Chapter 11. Szegő kernel asymptotics on some non-compact CR manifolds Memoirs of the American Mathematical Society, no. 1217. Chin-Yu Hsiao.

### Abstract:

Let $X$ be an abstract not necessarily compact orientable CR manifold of dimension $2n-1$, $n\geqslant 2$, and let $L^k$ be the $k$-th tensor power of a CR complex line bundle $L$ over $X$. Given  Read more...

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