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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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Alice Oswald
Hardcover
R681
Discovery Miles 6 810
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