Calviño-Louzao, Esteban.
Aspects of Differential Geometry V [electronic resource] / by Esteban Calviño-Louzao, Eduardo García-Río, Peter Gilkey, JeongHyeong Park, Ramón Vázquez-Lorenzo. - 1st ed. 2021. - XVI, 140 p. online resource. - Synthesis Lectures on Mathematics & Statistics, 1938-1751 . - Synthesis Lectures on Mathematics & Statistics, .
Preface -- Acknowledgments -- Functional Analysis -- Elliptic Operator Theory -- Potential Theory -- Complex Geometry -- Bibliography -- Authors' Biographies -- Index.
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.
9783031024320
10.1007/978-3-031-02432-0 doi
Mathematics.
Statistics .
Engineering mathematics.
Mathematics.
Statistics.
Engineering Mathematics.
QA1-939
510
Aspects of Differential Geometry V [electronic resource] / by Esteban Calviño-Louzao, Eduardo García-Río, Peter Gilkey, JeongHyeong Park, Ramón Vázquez-Lorenzo. - 1st ed. 2021. - XVI, 140 p. online resource. - Synthesis Lectures on Mathematics & Statistics, 1938-1751 . - Synthesis Lectures on Mathematics & Statistics, .
Preface -- Acknowledgments -- Functional Analysis -- Elliptic Operator Theory -- Potential Theory -- Complex Geometry -- Bibliography -- Authors' Biographies -- Index.
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.
9783031024320
10.1007/978-3-031-02432-0 doi
Mathematics.
Statistics .
Engineering mathematics.
Mathematics.
Statistics.
Engineering Mathematics.
QA1-939
510