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010   $a3-642-23840-8
024 7 $a10.1007/978-3-642-23840-6
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035   $a(DE-He213)978-3-642-23840-6
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100   $a20120104d2012      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aSpectral Analysis on Graph-like Spaces$b[electronic resource] /$fby Olaf Post
205   $a1st ed. 2012.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2012.
215   $a1 online resource (XV, 431 p. 28 illus.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2039
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-642-23839-4 
320   $aIncludes bibliographical references and index.
327   $a1 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.
330   $aSmall-radius tubular structures have attracted considerable attention in the last few years, and are frequently used in different areas such as Mathematical Physics, Spectral Geometry and Global Analysis.   In this monograph, we analyse Laplace-like operators on thin tubular structures ("graph-like spaces''), and their natural limits on metric graphs. In particular, we explore norm resolvent convergence, convergence of the spectra and resonances.   Since the underlying spaces in the thin radius limit change, and become singular in the limit, we develop new tools such as   -norm convergence of operators acting in different Hilbert  spaces,   - an extension of the concept of boundary triples to partial  differential operators, and   -an abstract definition of resonances via boundary triples.   These tools are formulated in an abstract framework, independent of the original problem of graph-like spaces, so that they can be applied in many other situations where the spaces are perturbed.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v2039
606   $aMathematical analysis
606   $aAnalysis (Mathematics)
606   $aFunctional analysis
606   $aOperator theory
606   $aMathematical physics
606   $aPartial differential equations
606   $aGraph theory
606   $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
606   $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139
606   $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
606   $aGraph Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M29020
615  0$aMathematical analysis.
615  0$aAnalysis (Mathematics).
615  0$aFunctional analysis.
615  0$aOperator theory.
615  0$aMathematical physics.
615  0$aPartial differential equations.
615  0$aGraph theory.
615 14$aAnalysis.
615 24$aFunctional Analysis.
615 24$aOperator Theory.
615 24$aMathematical Physics.
615 24$aPartial Differential Equations.
615 24$aGraph Theory.
676   $a515
700   $aPost$b Olaf$4aut$4http://id.loc.gov/vocabulary/relators/aut$0477397
906   $aBOOK
912   $a996466637103316
996   $aSpectral analysis on graph-like spaces$9239891
997   $aUNISA