000			05023nam a22004213i 4500
001			EBC5501873
003			MiAaPQ
005			20240724113326.0
006			m o d |
007			cr cnu||||||||
008			240724s2018 xx o ||||0 eng d
020			_a9781470447502 _q(electronic bk.)
020			_z9781470441012
035			_a(MiAaPQ)EBC5501873
035			_a(Au-PeEL)EBL5501873
035			_a(OCoLC)1039082787
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
100	1		_aHsiao, Chin-Yu.
245	1	0	_aSzegő Kernel Asymptotics for High Power of CR Line Bundles and Kodaira Embedding Theorems on CR Manifolds.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2018.
264		4	_c©2018.
300			_a1 online resource (154 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society Series ; _vv.254
505	0		_aCover -- 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 -- Chapter 4. Semi-classical \Box^{( )}_{ , } and the characteristic manifold for \Box^{( )}_{ , } -- Chapter 5. The heat equation for the local operatot \Box^{( )}_{ } -- 5.1. \Box^{( )}_{ } and the eikonal equation for \Box^{( )}_{ } -- 5.2. The transport equations for \Box^{( )}_{ } -- 5.3. Microlocal Hodge decomposition theorems for \Box^{( )}_{ } in -- 5.4. The tangential Hessian of ( , , ) -- Chapter 6. Semi-classical Hodge decomposition theorems for \Box^{( )}_{ , } in some non-degenerate part of Σ -- Chapter 7. Szegö kernel asymptotics for lower energy forms -- 7.1. Asymptotic upper bounds -- 7.2. 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 -- 11.1. The partial Fourier transform and the operator ^{( )}_{ , } -- 11.2. The small spectral gap property for \Box⁽⁰⁾_{ , } with respect to ⁽⁰⁾_{ , }.
505	8		_a11.3. Szegő kernel asymptotics on Γ×\Real, where Γ=\Complexⁿ⁻¹ or Γ is a bounded strongly pseudoconvex domain in \Complexⁿ⁻¹ -- Chapter 12. The proof of Theorem 5.28 -- References -- Back Cover.
520			_aLet 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 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_k\Pi ^{(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.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
655		4	_aElectronic books.
776	0	8	_iPrint version: _aHsiao, Chin-Yu _tSzegő Kernel Asymptotics for High Power of CR Line Bundles and Kodaira Embedding Theorems on CR Manifolds _dProvidence : American Mathematical Society,c2018 _z9781470441012
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society Series
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5501873 _zClick to View
999			_c4674 _d4674