| Description |
1 online resource (158 p.) |
| Series |
Synthesis Lectures on Mathematics and Statistics Ser |
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Synthesis lectures on mathematics and statistics.
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| Contents |
16. Functional analysis -- 16.1. Basic concepts in geometry and topology -- 16.2. Banach and Fréchet spaces -- 16.3. Hilbert spaces -- 16.4. Spectral theory in a separable Hilbert space |
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17. Elliptic operator theory -- 17.1. Fourier transform -- 17.2. Sobolev spaces and the Rellich lemma -- 17.3. Norms on spaces of sections to a bundle -- 17.4. Spectrum of an operator of Laplace type |
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18. Potential theory -- 18.1. Operators of Dirac type -- 18.2. The de Rham complex -- 18.3. Spinors -- 18.4. The Dolbeault complex -- 18.5. Duality and vanishing theorems in complex geometry |
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19. Complex geometry -- 19.1. Introduction to holomorphic geometry -- 19.2. The geometry of complex projective space -- 19.3. Hodge manifolds -- 19.4. The Kodaira embedding theorem |
| Summary |
Book V completes the discussion of the first four books by treating in some detail the analytic results in elliptic operator theory used previously. Chapters 16 and 17 provide a treatment of the techniques in Hilbert space, the Fourier transform, and elliptic operator theory necessary to establish the spectral decomposition theorem of a self-adjoint operator of Laplace type and to prove the Hodge Decomposition Theorem that was stated without proof in Book II. In Chapter 18, we treat the de Rham complex and the Dolbeault complex, and discuss spinors. In Chapter 19, we discuss complex geometry and establish the Kodaira Embedding Theorem |
| Notes |
Print version record |
| Subject |
Geometry, Differential.
|
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Geometry, Differential
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| Form |
Electronic book
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| Author |
García-Río, Eduardo
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Gilkey, Peter B
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Park, Jeonghyeong
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Vázquez-Lorenzo, Ramón
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| ISBN |
1636391117 |
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9781636391113 |
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