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＜E-Book＞
Spectral Analysis on Graph-like Spaces / by Olaf Post
(Lecture Notes in Mathematics. ISSN:16179692 ; 2039)

Edition	1st ed. 2012.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	2012
Language	English
Size	XV, 431 p. 28 illus : online resource
Authors	*Post, Olaf author SpringerLink (Online service)
Subjects	LCSH:Mathematical analysis LCSH:Functional analysis LCSH:Operator theory LCSH:Mathematical physics LCSH:Differential equations LCSH:Graph theory FREE:Analysis FREE:Functional Analysis FREE:Operator Theory FREE:Mathematical Physics FREE:Differential Equations FREE:Graph Theory
Notes	1 Introduction -- 2 Graphs and associated Laplacians -- 3 Scales of Hilbert space and boundary triples -- 4 Two operators in different Hilbert spaces -- 5 Manifolds, tubular neighbourhoods and their perturbations -- 6 Plumber’s shop: Estimates for star graphs and related spaces -- 7 Global convergence results 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 HTTP:URL=https://doi.org/10.1007/978-3-642-23840-6

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