EAN: 9783642238390

SPECTRAL ANALYSIS ON GRAPH-LIKE SPACES - OLAF P...

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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