Szegő Kernel Asymptotics for High Power of CR Line Bundles and Kodaira Embedding Theorems on CR Manifolds. (Record no. 4674)
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| fixed length control field | 05023nam a22004213i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC5501873 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240724113326.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2018 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470447502 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470441012 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC5501873 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL5501873 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1039082787 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Hsiao, Chin-Yu. |
| 245 10 - TITLE STATEMENT | |
| Title | Szegő Kernel Asymptotics for High Power of CR Line Bundles and Kodaira Embedding Theorems on CR Manifolds. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2018. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2018. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (154 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society Series ; |
| Volume/sequential designation | v.254 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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 -- 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# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 11.3. 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 ## - SUMMARY, ETC. | |
| Summary, etc. | 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 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 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic 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 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Hsiao, Chin-Yu |
| Title | Szegő Kernel Asymptotics for High Power of CR Line Bundles and Kodaira Embedding Theorems on CR Manifolds |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2018 |
| International Standard Book Number | 9781470441012 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5501873">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5501873</a> |
| Public note | Click to View |
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