Keller, Matthias, Lenz, Daniel, Wojciechowski, Radosław K. 　著

目次

Part 0 Prelude.- Chapter 0 Finite graphs.- Part 1 Foundations and fundamental topics.- Chapter 1 Infinite graphs – key concepts.- Chapter 2 Infinite graphs – toolbox.- Chapter 3 Markov uniqueness and essential self-adjointness.- Chapter 4 Agmon–Allegretto–Piepenbrink and Persson theorems.- Chapter 5 Large time behavior of the heat kernel.- Chapter 6 Recurrence.- Chapter 7 Stochastic completeness.- Part 2 Classes of graphs.- Chapter 8 Uniformly positive measure.- Chapter 9 Weak spherical symmetry.- Chapter 10 Sparseness and isoperimetric inequalities.- Part 3 Geometry and intrinsic metrics.- Chapter 11 Intrinsic metrics: definition and basic facts.- Chapter 12 Harmonic functions and Caccioppoli theory.- Chapter 13 Spectral bounds.- Chapter 14 Volume growth criterion for stochastic completeness.- Appendix A The spectral theorem.- Appendix B Closed forms on Hilbert spaces.- Appendix C Dirichlet forms and Beurling–Deny criteria.- Appendix D Semigroups, resolvents and their generators.- Appendix E Aspects of operator theory.- Bibliography.- Index.- Notation Index.