000 | 03552nam a22005415i 4500 | ||
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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 |
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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. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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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 |