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9780821844717

Analysis on Graphs and its Applications

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  • ISBN13:

    9780821844717

  • ISBN10:

    0821844717

  • Format: Hardcover
  • Copyright: 2008-09-30
  • Publisher: Amer Mathematical Society

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Summary

This book addresses a new interdisciplinary area emerging on the border between various areas of mathematics, physics, chemistry, nanotechnology, and computer science. The focus here is on problems and techniques related to graphs, quantum graphs, and fractals that parallel those from differential equations, differential geometry, or geometric analysis. Also included are such diverse topics as number theory, geometric group theory, waveguide theory, quantum chaos, quantum wiresystems, carbon nano-structures, metal-insulator transition, computer vision, and communication networks.This volume contains a unique collection of expert reviews on the main directions in analysis on graphs (e.g., on discrete geometric analysis, zeta-functions on graphs, recently emerging connections between the geometric group theory and fractals, quantum graphs, quantum chaos on graphs, modeling waveguide systems and modeling quantum graph systems with waveguides, control theory on graphs), as well as research articles.

Table of Contents

Analysis on combinatorial graphs: Review articles: Nodal domains on graphs–How to count them and why?
Zeta functions of weighted graphs and covering graphs
Discrete geometric analysis
Research articles: Uniform existence of the integrated density of states for combinatorial and metric graphs over $Z^d$
Bartholdi zeta functions for periodic simple graphs
Asymptotic properties of Markov processes on Cayley trees
Analysis on fractals: Review articles: Groups and analysis on fractals
Research articles: Schreier spectrum of the Hanoi Towers group on three pegs
On the dichotomy in the heat kernel two sided estimates
Tube formulas for self-similar fractals
Existence of Eigenforms on nicely separated fractals
Analysis on quantum graphs: Review articles: Trace formulae for quantum graphs
Quantum graphs with spin Hamiltonians
Quantum graphs and quantum chaos
Quantum graphs: An Introduction and a brief survey
Research articles: Two constructions of quantum graphs and two types of spectral statistics
An example on the discrete spectrum of a star graph
The HELP inequality on trees
Boundary value problems for infinite metric graphs
Remarks about Hardy inequalities on metric trees
On the spectral gap in Andreev graphs
An inverse spectral problem for Sturm-Liouville operators with singular potentials on star-type graphs
Optimal Wegner estimates for random Schrodinger operators on metric graphs
Contraction semigroups on metric graphs
Localization in a quasiperiodic model on quantum graphs
Equilateral quantum graphs and boundary triples
A conditionally convergent trace formula for quantum graphs
Applications: Review articles: Control problems on quantum graphs
Leaky quantum graphs: A review
Thin tubes in mathematical physics, global analysis and spectral geometry
Simulation of quantum graphs by microwave networks
Twisting versus bending in quantum waveguides
Research articles: Quantum field theory on star graphs
On the skeleton method and an application to a quantum scissor
Vacuum energy and closed orbits in quantum graphs
Spectra of graphs and semi-conducting polymers
Table of Contents provided by Publisher. All Rights Reserved.

Supplemental Materials

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