000 03552nam a22005415i 4500
001 978-3-642-23840-6
003 DE-He213
005 20190213151303.0
007 cr nn 008mamaa
008 120104s2012 gw | s |||| 0|eng d
020 _a9783642238406
_9978-3-642-23840-6
024 7 _a10.1007/978-3-642-23840-6
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBK
_2thema
082 0 4 _a515
_223
100 1 _aPost, Olaf.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aSpectral Analysis on Graph-like Spaces
_h[electronic resource] /
_cby Olaf Post.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2012.
300 _aXV, 431 p. 28 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2039
505 0 _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.
520 _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.
650 0 _aGlobal analysis (Mathematics).
650 0 _aFunctional analysis.
650 0 _aOperator theory.
650 0 _aDifferential equations, partial.
650 1 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
650 2 4 _aFunctional Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12066
650 2 4 _aOperator Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M12139
650 2 4 _aMathematical Physics.
_0http://scigraph.springernature.com/things/product-market-codes/M35000
650 2 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
650 2 4 _aGraph Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M29020
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642238413
776 0 8 _iPrinted edition:
_z9783642238390
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2039
856 4 0 _uhttps://doi.org/10.1007/978-3-642-23840-6
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c10158
_d10158