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Spectral Analysis on Graph-like Spaces [[electronic resource] /] / by Olaf Post



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Autore: Post Olaf Visualizza persona
Titolo: Spectral Analysis on Graph-like Spaces [[electronic resource] /] / by Olaf Post Visualizza cluster
Pubblicazione: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2012
Edizione: 1st ed. 2012.
Descrizione fisica: 1 online resource (XV, 431 p. 28 illus.)
Disciplina: 515
Soggetto topico: Mathematical analysis
Analysis (Mathematics)
Functional analysis
Operator theory
Mathematical physics
Partial differential equations
Graph theory
Analysis
Functional Analysis
Operator Theory
Mathematical Physics
Partial Differential Equations
Graph Theory
Note generali: Bibliographic Level Mode of Issuance: Monograph
Nota di bibliografia: Includes bibliographical references and index.
Nota di contenuto: 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.
Sommario/riassunto: 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.
Titolo autorizzato: Spectral analysis on graph-like spaces  Visualizza cluster
ISBN: 3-642-23840-8
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 996466637103316
Lo trovi qui: Univ. di Salerno
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Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 2039