Aspects of Differential Geometry V
Seiten
2021
Morgan & Claypool Publishers (Verlag)
978-1-63639-112-0 (ISBN)
Morgan & Claypool Publishers (Verlag)
978-1-63639-112-0 (ISBN)
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Explores in detail analytic results in elliptic operator theory. The book provides 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.
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.
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.
Preface
Acknowledgments
Functional Analysis
Elliptic Operator Theory
Potential Theory
Complex Geometry
Bibliography
Authors' Biographies
Index
| Erscheinungsdatum | 07.05.2021 |
|---|---|
| Reihe/Serie | Synthesis Lectures on Mathematics and Statistics |
| Verlagsort | San Rafael |
| Sprache | englisch |
| Maße | 191 x 235 mm |
| Gewicht | 333 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-63639-112-5 / 1636391125 |
| ISBN-13 | 978-1-63639-112-0 / 9781636391120 |
| Zustand | Neuware |
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