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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 蕭欽玉 | zh_TW |
| dc.contributor.advisor | Chin-Yu Hsiao | en |
| dc.contributor.author | 蔡以心 | zh_TW |
| dc.contributor.author | Yi-Hsin Tsai | en |
| dc.date.accessioned | 2025-07-09T16:11:48Z | - |
| dc.date.available | 2025-07-10 | - |
| dc.date.copyright | 2025-07-09 | - |
| dc.date.issued | 2025 | - |
| dc.date.submitted | 2025-07-01 | - |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/97640 | - |
| dc.description.abstract | 在本論文中，我們引入了具有局部性光譜間隙的複流形並利用縮放方法研究其伯格曼核和譜核且得到其漸近。 透過這些漸近，我們給出了滿足局部譜間隙條件的全純厄米軌線叢的伯格曼核的漸近行為。並且，我們透過對縮放伯格曼核的觀察及靜相公式建立了一個伯格曼核及拓譜立茲量化算子全漸近展開。 此外，我們建立了有關擬微分算子的拓譜立茲算子的變形量化。 | zh_TW |
| dc.description.abstract | In this thesis, we introduce complex manifolds with local spectral gap and study their asymptotic behavior by using scaling method. With these asymptotic, we obtain an asymptotic expansion for the Bergman kernel of a Hermitian holomorphic orbifold line bundle satisfying the local spectral gap condition. Furthermore, we establish the full asymptotic expansion of both the Bergman kernel and the Toeplitz operator, using the observations of the scaled Bergman kernel and the stationary phase formula. In addition, we establish the deformation quantization for Toeplitz operators with pseudodifferential operators. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2025-07-09T16:11:48Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2025-07-09T16:11:48Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | Acknowledgements i
摘要 iii Abstract v Contents vii Chapter I Introduction 1 I.1 Main Results and Applications . . . . . . . . . . . . . . . . . . . 6 Chapter II Preliminaries 17 II.1 Basic Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 II.2 Complex Manifold . . . . . . . . . . . . . . . . . . . . . . . . . . 18 II.3 Differential Operators . . . . . . . . . . . . . . . . . . . . . . . . 23 II.4 Bergman Kernel . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 II.5 Stationary Phase Formula . . . . . . . . . . . . . . . . . . . . . . 31 Chapter III Asymptotic Behavior of Bergman Kernels on Complex Manifolds 35 III.1 Euclidean Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 III.2 Compact Manifold Case . . . . . . . . . . . . . . . . . . . . . . . 44 III.3 Manifold Case Without Spectral Gap . . . . . . . . . . . . . . . . 54 Chapter IV Asymptotic Behavior of Bergman Kernels on Complex Orbifold 61 IV.1 Notation and Set-up . . . . . . . . . . . . . . . . . . . . . . . . . 62 IV.2 Proof of Theorem IV.4 . . . . . . . . . . . . . . . . . . . . . . . . 68 IV.3 Kodaira Baily Embedding Theorem . . . . . . . . . . . . . . . . . 72 IV.4 Toeplitz Operator . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Chapter V Full Expansion 79 V.1 Bergman Kernel . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 V.1.1 Euclidean Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 V.1.2 Manifold Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 V.2 Toeplitz Operator . . . . . . . . . . . . . . . . . . . . . . . . . . 88 V.3 Toeplitz Operator with Pseudodifferential Operator . . . . . . . . 94 V.3.1 Euclidean Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 V.3.2 Manifold Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 References 107 | - |
| dc.language.iso | en | - |
| dc.subject | 複幾何 | zh_TW |
| dc.subject | 變形量化 | zh_TW |
| dc.subject | 軌形 | zh_TW |
| dc.subject | 擬微分算子 | zh_TW |
| dc.subject | 半古典分析 | zh_TW |
| dc.subject | 拓譜立茲算子 | zh_TW |
| dc.subject | 伯格曼核 | zh_TW |
| dc.subject | Toeplitz Operator | en |
| dc.subject | Bergman Kernel | en |
| dc.subject | Complex Geometry | en |
| dc.subject | Deformation Quantization | en |
| dc.subject | Orbifold | en |
| dc.subject | Pseudodifferential Operator | en |
| dc.subject | Semi-Classical Analysis | en |
| dc.title | 複流形及軌形上的拓譜立茲量化之半經典漸近 | zh_TW |
| dc.title | Semi-Classical Asymptotic Expansions for Toeplitz Quantizations on Complex Manifolds and Orbifolds | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 113-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 王金龍;黃榮宗 | zh_TW |
| dc.contributor.oralexamcommittee | Chin-Lung Wang;Rung-Tzung Huang | en |
| dc.subject.keyword | 伯格曼核,複幾何,變形量化,軌形,擬微分算子,半古典分析,拓譜立茲算子, | zh_TW |
| dc.subject.keyword | Bergman Kernel,Complex Geometry,Deformation Quantization,Orbifold,Pseudodifferential Operator,Semi-Classical Analysis,Toeplitz Operator, | en |
| dc.relation.page | 114 | - |
| dc.identifier.doi | 10.6342/NTU202501014 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2025-07-02 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 數學系 | - |
| dc.date.embargo-lift | 2025-07-10 | - |
| 顯示於系所單位： | 數學系 | |
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