Aspects of Differential Geometry V by Esteban Calviolouzao

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Summary

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.

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Aspects of Differential Geometry V by Esteban Calviolouzao

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.
Gilkey, Peter: - Peter B Gilkey is a Professor of Mathematics and a member of the Institute of Theoretical Science at the University of Oregon. He is a fellow of the American Mathematical Society and is a member of the editorial board of Results in Mathematics, Differential Geometry and its Applications, and The Journal of Geometric Analysis. He received his Ph.D. in 1972 from Harvard University under the direction of L. Nirenberg. His research specialties are Differential Geometry, Elliptic Partial Differential Equations, and Algebraic topology. He has published more than 260 research articles and books.
SKU Unavailable
ISBN 13 9783031013041
ISBN 10 3031013042
Title Aspects of Differential Geometry V
Author Peter Gilkey
Series Synthesis Lectures On Mathematics And Statistics Ser
Condition Unavailable
Binding Type Paperback
Publisher Springer International Publishing AG
Year published 2021-04-06
Number of pages 140
Cover note Book picture is for illustrative purposes only, actual binding, cover or edition may vary.