Analysis on Graphs and Its Applications (Proceedings of Symposia in Pure Mathematics No. 77)

Analysis on Graphs and Its Applications (Proceedings of Symposia in Pure Mathematics No. 77)

By: Pavel Exner (editor), Peter A. Kuchment (editor), Alexander Teplyaev (editor), Jonathan P. Keating (editor), Toshikazu Sunada (editor)Hardback

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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.

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Analysis on combinatorial graphs: Review articles: Nodal domains on graphs--How to count them and why? by R. Band, I. Oren, and U. Smilansky Zeta functions of weighted graphs and covering graphs by M. D. Horton, H. M. Stark, and A. A. Terras Discrete geometric analysis by T. Sunada Research articles: Uniform existence of the integrated density of states for combinatorial and metric graphs over $Z^d$ by M. J. Gruber, D. H. Lenz, and I. Veselic Bartholdi zeta functions for periodic simple graphs by D. Guido, T. Isola, and M. L. Lapidus Asymptotic properties of Markov processes on Cayley trees by M. Kelbert and Y. Suhov Analysis on fractals: Review articles: Group and analysis on fractals by V. Nekrashevych and A. Teplyaev Research articles: Schreier spectrum of the Hanoi Towers group on three pegs by R. Grigorchuk and Z. Sunic On the dichotomy in the heat kernel two sided estimates by A. Grigor'yan and T. Kumagai Tube formulas for self-simlar fractals by M. L. Lapidus and E. P. J. Pearse Existence of Eigenforms on nicely separated fractals by R. Peirone Analysis on quantum graphs: Review articles: Trace formulae for quantum graphs by J. Bolte and S. Endres Quantum graphs with spin Hamiltonians by J. Harrison Quantum graphs and quantum chaos by J. P. Keating Quantum graphs: An introduction and a brief survey by P. Kuchment Research articles: Two constructions of quantum graphs and two types of spectral statistics by G. Berkolaik An example on the discrete spectrum of a star graph by B. M. Brown, M. S. P. Eastham, and I. G. Wood The HELP inequality on trees by B. M. Brown, M. Langer, and K. M. Schmidt Boundary value problems for infnite metric graphs by R. Carlson Remarks about Hardy inequalities on metric trees by T. Ekholm, R. L. Frank, and H. Kovarik On the spectral gap in Andreev graphs by H. Flechsig and S. Gnutzmann An inverse spectral problem for Sturm-Liouville operators with singular potentials on star-type graphs by G. Freiling, M. Ignatiev, and V. Yurko Optimal Wegner estimates for random Schrodinger operators on metric graphs by M. J. Gruber, M. Helm, and I. Veselic Contraction semigroups on metric graphs by V. Kostrykin, J. Potthoff, and R. Schrader Localization in a quasiperiodic model on quantum graphs by K. Pankrashkin Equilateral quantum graphs and boundary triples by O. Post A conditionally convergent trace formula for quantum graphs by B. Winn Applications: Review articles: Conrol problems on quantum graphs by S. Avdonin Leaky quantum graphs: A review by P. Exner Thin tubes in mathematical physics, global analysis and spectral geometry by D. Grieser Simulation of quantum graphs by microwave networks by O. Hul, M. Lawniczak, S. Bauch, and L. Sirko Twisting versus bending in quantum waveguides by D. Krejcirik Research articles: Quantum field theory on star graphs by B. Bellazzini, M. Burrello, M. Mintchev, and P. Sorba On the skeleton method and an application to a quantum scissor by H. D. Comean, P. Duclos, and B. Ricaud Vacuum energy and closed orbits in quantum graphs by S. A. Fulling and J. H. Wilson Spectra of graphs and semi-conducting polymers by P. Schapotschnikow and S. Gnutzmann.

Product Details

  • publication date: 15/11/2008
  • ISBN13: 9780821844717
  • Format: Hardback
  • Number Of Pages: 689
  • ID: 9780821844717
  • weight: 1431
  • ISBN10: 0821844717

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