| 书目名称 | The Geometry of Domains in Space | | 编辑 | Steven G. Krantz,Harold R. Parks | | 视频video | | | 丛书名称 | Birkhäuser Advanced Texts‘ Basler Lehrbücher | | 图书封面 |  | | 描述 | The analysis of Euclidean space is well-developed. The classical Lie groups that act naturally on Euclidean space-the rotations, dilations, and trans lations-have both shaped and guided this development. In particular, the Fourier transform and the theory of translation invariant operators (convolution transforms) have played a central role in this analysis. Much modern work in analysis takes place on a domain in space. In this context the tools, perforce, must be different. No longer can we expect there to be symmetries. Correspondingly, there is no longer any natural way to apply the Fourier transform. Pseudodifferential operators and Fourier integral operators can playa role in solving some of the problems, but other problems require new, more geometric, ideas. At a more basic level, the analysis of a smoothly bounded domain in space requires a great deal of preliminary spadework. Tubular neighbor hoods, the second fundamental form, the notion of "positive reach", and the implicit function theorem are just some of the tools that need to be invoked regularly to set up this analysis. The normal and tangent bundles become part of the language of classical analysis when that analy | | 出版日期 | Textbook 1999 | | 关键词 | Eigenvalue; Finite; Fundamental theorem of calculus; Mean curvature; Sobolev space; calculus; curvature; di | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4612-1574-5 | | isbn_softcover | 978-1-4612-7199-4 | | isbn_ebook | 978-1-4612-1574-5Series ISSN 1019-6242 Series E-ISSN 2296-4894 | | issn_series | 1019-6242 | | copyright | Springer Science+Business Media New York 1999 |
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发表于 2025-3-21 18:14:56
