TY  - BOOK
AU  - Post,Olaf
ED  - SpringerLink (Online service)
TI  - Spectral Analysis on Graph-like Spaces
T2  - Lecture Notes in Mathematics,
SN  - 9783642238406
AV  - QA299.6-433 
U1  - 515 23
PY  - 2012///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Global analysis (Mathematics)
KW  - Functional analysis
KW  - Operator theory
KW  - Differential equations, partial
KW  - Analysis
KW  - Functional Analysis
KW  - Operator Theory
KW  - Mathematical Physics
KW  - Partial Differential Equations
KW  - Graph Theory
N1  - 1 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
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-642-23840-6
ER  -