| 书目名称 | Spectral Analysis on Graph-like Spaces | | 编辑 | Olaf Post | | 视频video | | | 概述 | A thorough analysis of quantum graphs and their approximations (graph-like spaces).A self-contained explanation of the tools needed (convergence of operators in different spaces, boundary triples).The | | 丛书名称 | Lecture Notes in Mathematics | | 图书封面 |  | | 描述 | Small-radius tubular structures have attracted considerable attention in the last few years, and are frequently used in different areas such as Mathematical Physics, Spectral Geometry and Global Analysis. In this monograph, we analyse Laplace-like operators on thin tubular structures ("graph-like spaces‘‘), and their natural limits on metric graphs. In particular, we explore norm resolvent convergence, convergence of the spectra and resonances. Since the underlying spaces in the thin radius limit change, and become singular in the limit, we develop new tools such as norm convergence of operators acting in different Hilbert spaces, an extension of the concept of boundary triples to partial differential operators, and an abstract definition of resonances via boundary triples. These tools are formulated in an abstract framework, independent of the original problem of graph-like spaces, so that they can be applied in many other situations where the spaces are perturbed. | | 出版日期 | Book 2012 | | 关键词 | 35PXX ; 47A10 ; 35J25; 05C50; 34B45; 47F05; 58J50; boundary triples; convergence of operators in diffe | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-23840-6 | | isbn_softcover | 978-3-642-23839-0 | | isbn_ebook | 978-3-642-23840-6Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | Springer-Verlag Berlin Heidelberg 2012 |
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发表于 2025-3-21 16:42:30
