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Analysis on Graphs and Its Applications
About this Title
Pavel Exner, Academy of Sciences, Rez near Prague, Czech Republic, Jonathan P. Keating, University of Bristol, Clifton, Bristol, United Kingdom, Peter Kuchment, Texas A & M University, College Station, TX, Toshikazu Sunada, Meiji University, Kawasaki, Japan and Alexander Teplyaev, University of Connecticut, Storrs, CT, Editors
Publication: Proceedings of Symposia in Pure Mathematics
Publication Year:
2008; Volume 77
ISBNs: 978-0-8218-4471-7 (print); 978-0-8218-9384-5 (online)
DOI: https://doi.org/10.1090/pspum/077
ReadershipTable of Contents
Download chapters as PDF
Front/Back Matter
Chapter 1. Analysis on combinatorial graphs
Review articles
- Ram Band, Idan Oren and Uzy Smilansky – Nodal domains on graphs—how to count them and why? [MR 2459862]
- Matthew D. Horton, H. M. Stark and Audrey A. Terras – Zeta functions of weighted graphs and covering graphs [MR 2459863]
- Toshikazu Sunada – Discrete geometric analysis [MR 2459864]
Research articles
- Michael J. Gruber, Daniel H. Lenz and Ivan Veselić – Uniform existence of the integrated density of states for combinatorial and metric graphs over $\mathbb {Z}^d$ [MR 2459865]
- Daniele Guido, Tommaso Isola and Michel L. Lapidus – Bartholdi zeta functions for periodic simple graphs [MR 2459866]
- M. Kelbert and Y. Suhov – Asymptotic properties of Markov processes on Cayley trees [MR 2459867]
Chapter 2. Analysis on fractals
Review articles
- Volodymyr Nekrashevych and Alexander Teplyaev – Groups and analysis on fractals [MR 2459868]
Research articles
- Rostislav Grigorchuk and Zoran Šunić – Schreier spectrum of the Hanoi Towers group on three pegs [MR 2459869]
- Alexander Grigor′yan and Takashi Kumagai – On the dichotomy in the heat kernel two sided estimates [MR 2459870]
- Michel L. Lapidus and Erin P. J. Pearse – Tube formulas for self-similar fractals [MR 2459871]
- Roberto Peirone – Existence of eigenforms on nicely separated fractals [MR 2459872]
Chapter 3. Analysis on quantum graphs
Review articles
- Jens Bolte and Sebastian Endres – Trace formulae for quantum graphs [MR 2459873]
- J. M. Harrison – Quantum graphs with spin Hamiltonians [MR 2459874]
- J. P. Keating – Quantum graphs and quantum chaos [MR 2459875]
- Peter Kuchment – Quantum graphs: An introduction and a brief survey [MR 2459876]
Research articles
- G. Berkolaiko – Two constructions of quantum graphs and two types of spectral statistics [MR 2459877]
- B. M. Brown, M. S. P. Eastham and I. G. Wood – An example on the discrete spectrum of a star graph [MR 2459878]
- B. Malcolm Brown, Matthias Langer and Karl Michael Schmidt – The HELP inequality on trees [MR 2459879]
- Robert Carlson – Boundary value problems for infinite metric graphs [MR 2459880]
- Tomas Ekholm, Rupert L. Frank and Hynek Kovařík – Remarks about Hardy inequalities on metric trees [MR 2459881]
- Holger Flechsig and Sven Gnutzmann – On the spectral gap in Andreev graphs [MR 2459882]
- G. Freiling, M. Ignatiev and V. Yurko – An inverse spectral problem for Sturm-Liouville operators with singular potentials on star-type graphs [MR 2459883]
- Michael J. Gruber, Mario Helm and Ivan Veselić – Optimal Wegner estimates for random Schrödinger operators on metric graphs [MR 2459884]
- Vadim Kostrykin, Jürgen Potthoff and Robert Schrader – Contraction semigroups on metric graphs [MR 2459885]
- Konstantin Pankrashkin – Localization in a quasiperiodic model on quantum graphs [MR 2459886]
- Olaf Post – Equilateral quantum graphs and boundary triples [MR 2459887]
- B. Winn – A conditionally convergent trace formula for quantum graphs [MR 2459888]
Chapter 4. Applications
Review articles
- Sergei Avdonin – Control problems on quantum graphs [MR 2459889]
- Pavel Exner – Leaky quantum graphs: A review [MR 2459890]
- Daniel Grieser – Thin tubes in mathematical physics, global analysis and spectral geometry [MR 2459891]
- Oleh Hul, Michał Ławniczak, Szymon Bauch and Leszek Sirko – Simulation of quantum graphs by microwave networks [MR 2459892]
- David Krejčiřík – Twisting versus bending in quantum waveguides [MR 2459893]
Research articles
- B. Bellazzini, M. Burrello, M. Mintchev and P. Sorba – Quantum field theory on star graphs [MR 2459894]
- H. D. Cornean, P. Duclos and B. Ricaud – On the skeleton method and an application to a quantum scissor [MR 2459895]
- S. A. Fulling and J. H. Wilson – Vacuum energy and closed orbits in quantum graphs [MR 2459896]
- Philipp Schapotschnikow and Sven Gnutzmann – Spectra of graphs and semi-conducting polymers [MR 2459897]