丸善のおすすめ度
Eigenfunctions of the Laplacian on a Riemannian Manifold(CBMS Regional Conference Series in Mathematics Vol. 125) P 394 p. 18
発行年月 |
2017年12月 |
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出版国 |
アメリカ合衆国 |
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言語 |
英語 |
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媒体 |
冊子 |
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装丁 |
paper |
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ページ数/巻数 |
394 p. |
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ジャンル |
洋書/理工学/数学/解析学 |
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ISBN |
9781470410377 |
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商品コード |
1026514965 |
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本の性格 |
学術書 |
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新刊案内掲載月 |
2018年01月 |
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商品URL
| https://kw.maruzen.co.jp/ims/itemDetail.html?itmCd=1026514965 |
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内容
Eigenfunctions of the Laplacian of a Riemannian manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates. This book is an introduction to both the local and global analysis of eigenfunctions. The local analysis of eigenfunctions pertains to the behavior of the eigenfunctions on wavelength scale balls. After re-scaling to a unit ball, the eigenfunctions resemble almost-harmonic functions. Global analysis refers to the use of wave equation methods to relate properties of eigenfunctions to properties of the geodesic flow.The emphasis is on the global methods and the use of Fourier integral operator methods to analyze norms and nodal sets of eigenfunctions. A somewhat unusual topic is the analytic continuation of eigenfunctions to Grauert tubes in the real analytic case, and the study of nodal sets in the complex domain.The book, which grew out of lectures given by the author at a CBMS conference in 2011, provides complete proofs of some model results, but more often it gives informal and intuitive explanations of proofs of fairly recent results. It conveys inter-related themes and results and offers an up-to-date comprehensive treatment of this important active area of research.