**Proceedings of Symposia in Pure Mathematics**

Volume: 77;
2008;
705 pp;
Hardcover

MSC: Primary 05; 11; 20; 28; 35; 47; 58; 68; 70; 78; 81;

Print ISBN: 978-0-8218-4471-7

Product Code: PSPUM/77

List Price: $139.00

Individual Member Price: $111.20

**Electronic ISBN: 978-0-8218-9384-5
Product Code: PSPUM/77.E**

List Price: $139.00

Individual Member Price: $111.20

# Analysis on Graphs and Its Applications

Share this page *Edited by *
*Pavel Exner; Jonathan P. Keating; Peter Kuchment; Toshikazu Sunada; Alexander Teplyaev*

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 wire systems, 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.

#### Readership

Graduate students and research mathematicians interested in various areas of analysis, dynamical systems, groups and their actions on graphs, mathematical physics.

# Table of Contents

## Analysis on Graphs and Its Applications

- Contents vii8 free
- Preface xi12 free
- Vladimir A. Geyler, April 29, 1943 - April 2, 2007 xiii14 free
- Chapter 1. Analysis on combinatorial graphs 116 free
- Chapter 2. Analysis on fractals 139154
- Chapter 3. Analysis on quantum graphs 243258
- Review articles 245260
- Research articles 313328
- Two constructions of quantum graphs and two types of spectral statistics 315330
- An example on the discrete spectrum of a star graph 331346
- The HELP inequality on trees 337352
- Boundary value problems for infinite metric graphs 355370
- Remarks about Hardy inequalities on metric trees 369384
- On the spectral gap in Andreev graphs 381396
- An inverse spectral problem for Sturm-Liouville operators with singular potentials on star-type graphs 397412
- Optimal Wegner estimates for random Schrödinger operators on metric graphs 409424
- Contraction semigroups on metric graphs 423438
- Localization in a quasiperiodic model on quantum graphs 459474
- Equilateral quantum graphs and boundary triples 469484
- A conditionally convergent trace formula for quantum graphs 491506

- Chapter 4. Applications 503518