书目名称 | Inverse Spectral and Scattering Theory |
副标题 | An Introduction |
编辑 | Hiroshi Isozaki |
视频video | |
概述 | Is the first book on multi-dimensional spectral theory and inverse scattering on non-compact manifolds.Serves as a comprehensive introductory guide to PDEs, with minimal preparatory knowledge of mathe |
丛书名称 | SpringerBriefs in Mathematical Physics |
图书封面 |  |
描述 | The aim of this book is to provide basic knowledge of the inverse problems arising in various areas in mathematics, physics, engineering, and medical science. These practical problems boil down to the mathematical question in which one tries to recover the operator (coefficients) or the domain (manifolds) from spectral data. The characteristic properties of the operators in question are often reduced to those of Schrödinger operators. We start from the 1-dimensional theory to observe the main features of inverse spectral problems and then proceed to multi-dimensions. The first milestone is the Borg–Levinson theorem in the inverse Dirichlet problem in a bounded domain elucidating basic motivation of the inverse problem as well as the difference between 1-dimension and multi-dimension. The main theme is the inverse scattering, in which the spectral data is Heisenberg’s S-matrix defined through the observation of the asymptotic behavior at infinity of solutions. Significant progress has been made in the past 30 years by using the Faddeev–Green function or the complex geometrical optics solution by Sylvester and Uhlmann, which made it possible to reconstruct the potential from the S-ma |
出版日期 | Book 2020 |
关键词 | Inverse spectral problem; Inverse scattering; Faddeev’s Green function; complex geometrical optics solu |
版次 | 1 |
doi | https://doi.org/10.1007/978-981-15-8199-1 |
isbn_softcover | 978-981-15-8198-4 |
isbn_ebook | 978-981-15-8199-1Series ISSN 2197-1757 Series E-ISSN 2197-1765 |
issn_series | 2197-1757 |
copyright | The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2020 |