|
|
|
|
| LEADER |
02545nmm a2200397 u 4500 |
| 001 |
EB000387762 |
| 003 |
EBX01000000000000000240814 |
| 005 |
00000000000000.0 |
| 007 |
cr||||||||||||||||||||| |
| 008 |
130626 ||| eng |
| 020 |
|
|
|a 9783642238406
|
| 100 |
1 |
|
|a Post, Olaf
|
| 245 |
0 |
0 |
|a Spectral Analysis on Graph-like Spaces
|h Elektronische Ressource
|c by Olaf Post
|
| 250 |
|
|
|a 1st ed. 2012
|
| 260 |
|
|
|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 2012, 2012
|
| 300 |
|
|
|a XV, 431 p. 28 illus
|b online resource
|
| 505 |
0 |
|
|a 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
|
| 653 |
|
|
|a Functional analysis
|
| 653 |
|
|
|a Mathematical analysis
|
| 653 |
|
|
|a Functional Analysis
|
| 653 |
|
|
|a Analysis
|
| 653 |
|
|
|a Graph Theory
|
| 653 |
|
|
|a Mathematical Physics
|
| 653 |
|
|
|a Operator theory
|
| 653 |
|
|
|a Mathematical physics
|
| 653 |
|
|
|a Operator Theory
|
| 653 |
|
|
|a Graph theory
|
| 653 |
|
|
|a Differential Equations
|
| 653 |
|
|
|a Differential equations
|
| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
|
| 989 |
|
|
|b Springer
|a Springer eBooks 2005-
|
| 490 |
0 |
|
|a Lecture Notes in Mathematics
|
| 028 |
5 |
0 |
|a 10.1007/978-3-642-23840-6
|
| 856 |
4 |
0 |
|u https://doi.org/10.1007/978-3-642-23840-6?nosfx=y
|x Verlag
|3 Volltext
|
| 082 |
0 |
|
|a 515
|
| 520 |
|
|
|a 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
|