04254nam 22007815 450 99646663710331620200701022931.03-642-23840-810.1007/978-3-642-23840-6(CKB)3390000000021667(SSID)ssj0000610895(PQKBManifestationID)11973987(PQKBTitleCode)TC0000610895(PQKBWorkID)10644930(PQKB)10356187(DE-He213)978-3-642-23840-6(MiAaPQ)EBC3070566(PPN)159084814(EXLCZ)99339000000002166720120104d2012 u| 0engurnn|008mamaatxtccrSpectral Analysis on Graph-like Spaces[electronic resource] /by Olaf Post1st ed. 2012.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2012.1 online resource (XV, 431 p. 28 illus.) Lecture Notes in Mathematics,0075-8434 ;2039Bibliographic Level Mode of Issuance: Monograph3-642-23839-4 Includes bibliographical references and index.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.Lecture Notes in Mathematics,0075-8434 ;2039Mathematical analysisAnalysis (Mathematics)Functional analysisOperator theoryMathematical physicsPartial differential equationsGraph theoryAnalysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12007Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Operator Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12139Mathematical Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/M35000Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Graph Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M29020Mathematical 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.515Post Olafauthttp://id.loc.gov/vocabulary/relators/aut477397BOOK996466637103316Spectral analysis on graph-like spaces239891UNISA