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Eigenfunctions of the Laplacian of a Riemannian manifold / Steve Zelditch.
Math/Physics/Astronomy Library QA1 .R33 no.125
Available
- Format:
- Book
- Author/Creator:
- Zelditch, Steven, 1953- author.
- Series:
- Regional conference series in mathematics ; no. 125.
- Conference Board of the Mathematical Sciences. Regional conference series in mathematics ; number 125
- Language:
- English
- Subjects (All):
- Riemannian manifolds.
- Eigenfunctions.
- Laplacian operator.
- Physical Description:
- xiv, 394 pages : illustrations ; 26 cm.
- Place of Publication:
- Providence, Rhode Island : Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, with the support from the National Science Foundation, [2017]
- Summary:
- 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.
- Notes:
- Based on the author's notes from his presentation at the NSF-CBMS Regional Conference in the Mathematical Sciences on Global Harmonic Analysis, held at University of Kentucky, June 20-24, 2011.
- Includes bibliographical references and index.
- ISBN:
- 9781470410377
- 1470410370
- OCLC:
- 1006524790
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