Spectral Analysis on Graph-like Spaces

• Main Author: Post, Olaf (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2012.
• Series: Lecture Notes in Mathematics, 2039
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Functional analysis.; Operator theory.; Partial differential equations.; Graph theory.; Mathematical physics.; Analysis.; Functional Analysis.; Operator Theory.; Mathematical Physics.; Partial Differential Equations.; Graph Theory.

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-...

Table of Contents:

• 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.