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Spectral analysis on graph-like spaces

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-...

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Autor principal: Post, Olaf
Lenguaje:eng
Publicado: Springer 2012
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-642-23840-6
http://cds.cern.ch/record/1691793
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author Post, Olaf
author_facet Post, Olaf
author_sort Post, Olaf
collection CERN
description 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.
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spelling cern-16917932021-04-21T21:07:01Zdoi:10.1007/978-3-642-23840-6http://cds.cern.ch/record/1691793engPost, OlafSpectral analysis on graph-like spacesMathematical Physics and MathematicsSmall-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.Springeroai:cds.cern.ch:16917932012
spellingShingle Mathematical Physics and Mathematics
Post, Olaf
Spectral analysis on graph-like spaces
title Spectral analysis on graph-like spaces
title_full Spectral analysis on graph-like spaces
title_fullStr Spectral analysis on graph-like spaces
title_full_unstemmed Spectral analysis on graph-like spaces
title_short Spectral analysis on graph-like spaces
title_sort spectral analysis on graph-like spaces
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-642-23840-6
http://cds.cern.ch/record/1691793
work_keys_str_mv AT postolaf spectralanalysisongraphlikespaces