@article{CML_2010__2_3_333_0, author = {Torki-Hamza, Nabila}, title = {Laplaciens de graphes infinis {I,} graphes m\'etriquement complets}, journal = {Confluentes Mathematici}, pages = {333--350}, publisher = {World Scientific Publishing Co Pte Ltd}, volume = {2}, number = {3}, year = {2010}, doi = {10.1142/S179374421000020X}, language = {fr}, url = {https://www.numdam.org/articles/10.1142/S179374421000020X/} }
TY - JOUR AU - Torki-Hamza, Nabila TI - Laplaciens de graphes infinis I, graphes métriquement complets JO - Confluentes Mathematici PY - 2010 SP - 333 EP - 350 VL - 2 IS - 3 PB - World Scientific Publishing Co Pte Ltd UR - https://www.numdam.org/articles/10.1142/S179374421000020X/ DO - 10.1142/S179374421000020X LA - fr ID - CML_2010__2_3_333_0 ER -
%0 Journal Article %A Torki-Hamza, Nabila %T Laplaciens de graphes infinis I, graphes métriquement complets %J Confluentes Mathematici %D 2010 %P 333-350 %V 2 %N 3 %I World Scientific Publishing Co Pte Ltd %U https://www.numdam.org/articles/10.1142/S179374421000020X/ %R 10.1142/S179374421000020X %G fr %F CML_2010__2_3_333_0
Torki-Hamza, Nabila. Laplaciens de graphes infinis I, graphes métriquement complets. Confluentes Mathematici, Tome 2 (2010) no. 3, pp. 333-350. doi : 10.1142/S179374421000020X. https://www.numdam.org/articles/10.1142/S179374421000020X/
[1] M. Braverman, O. Milatovic et and M. Shubin, Russ. Math. Surv. 57, 641 (2002), DOI : 10.1070/RM2002v057n04ABEH000532.
[2] R. Carlson, J. Diff. Eqns. 6, 1 (1998).
[3] P. Chernoff, J. Funct. Anal. 12, 401 (1973), DOI : 10.1016/0022-1236(73)90003-7.
[4] Y. Colin de Verdière , Spectre de Graphes , Cours Spécialisés 4 ( Société Mathématique de France , 1998 ) .
[5] Y. Colin de Verdière, N. Torki-Hamza et F. Truc, Essential self-adjointness for combinatorial Schrödinger operators II : Metrically non complete graphs , arXiv :1006.5778v1 .
[6] Y. Colin de Verdière, N. Torki-Hamza et F. Truc, Essential self-adjointness for combinatorial Schrödinger operators III : Magnetic fields, En préparation (2010) .
[7] J. Dodziuk, Analysis, Geometry and Topology of Elliptic Operators, ed. (World Scientific, 2006) pp. 353–368.
[8] P. Exner et al. , Analysis on Graphs and its Applications , Proc. Symp. Pure Math ( Amer. Math. Soc. , 2008 ) .
[9] M. Gaffney, Ann. Math. 60, 140 (1954), DOI : 10.2307/1969703.
[10] M. Gaffney, Ann. Math. 78, 426 (1955).
[11] S. Golénia et C. Schumacher, The problem of deficiency indices for discrete Schrödinger operators on locally finite graphs , arXiv :1005.0165v1 .
[12] P. E. T. Jorgensen, J. Math. Phys. 49(7), 073510 (2008), DOI : 10.1063/1.2953684.
[13] P. Kuchment, Quantum Graphs : An Introduction and a Brief Survey, Proc. Symp. Pure Math (AMS, 2008) pp. 291–314.
[14] G. Nenciu and I. Nenciu, Ann. Henri Poincaré 10, 377 (2009), DOI : 10.1007/s00023-009-0412-1.
[15] I. M. Oleinik, Mathematical Notes 54, 934 (1993), DOI : 10.1007/BF01209558.
[16] M. Reed et and B. Simon , Methods of Modern Mathematical Physics I, Functional Analysis , II, Fourier Analysis, Self-adjointness ( New York Academic Press , 1980 ) .
[17] M. Shubin, Geometric Aspects of Partial Differential Equations, Proc. Sympos (Amer. Math. Soc., Roskilde, Denmark, 1998) pp. 257–269.
[18] M. Shubin, J. Funct. Anal. 186, 92 (2001), DOI : 10.1006/jfan.2001.3778.
[19] R. Strichartz, J. Funct. Anal. 52, 48 (1983), DOI : 10.1016/0022-1236(83)90090-3.
[20] N. Torki-Hamza, Stabilité des valeurs propres avec champ magnétique sur une variété Riemannienne et sur un graphe, Thèse de doctorat de l’Université de Grenoble I, France (1989) .
[21] H. Weyl, Nachr. Kgl. Ges. Wiss. Göttingen. Math.-Phys. Kl. 37 (1909).
[22] A. Weber, Analysis of the Physical Laplacian and the Heat Flow on a Locally Finite Graph [math.SP] (2010) , arXiv :0801.0812v4 .
[23] R. K. Wojciechowski, Stochastic Completness of Graphs, Ph.D. Thesis, The graduate Center of the City University of New York (2008) .
- A graph without zero in its spectra, Analysis Mathematica, Volume 50 (2024) no. 4, p. 987 | DOI:10.1007/s10476-024-00056-3
- Magnetic cochains Laplacians and their essential self-adjointness, Discrete Mathematics, Algorithms and Applications, Volume 15 (2023) no. 05 | DOI:10.1142/s1793830922501233
- Weighted spectra on a weighted geometric realization of 2-simplexes and 3-simplexes, Discrete Mathematics, Algorithms and Applications, Volume 15 (2023) no. 05 | DOI:10.1142/s1793830922501300
- Essential self-adjointness of a weighted 3-simplicial complex Laplacians, Discrete Mathematics, Algorithms and Applications, Volume 15 (2023) no. 06 | DOI:10.1142/s1793830922501348
- A Glazman–Povzner–Wienholtz theorem on graphs, Advances in Mathematics, Volume 395 (2022), p. 108158 | DOI:10.1016/j.aim.2021.108158
- The magnetic discrete Laplacian inferred from the Gauß–Bonnet operator and application, Annals of Functional Analysis, Volume 12 (2021) no. 2 | DOI:10.1007/s43034-021-00119-8
- Self-adjointness of perturbed bi-Laplacians on infinite graphs, Indagationes Mathematicae, Volume 32 (2021) no. 2, p. 442 | DOI:10.1016/j.indag.2020.12.003
- m-accretive Laplacian on a non symmetric graph, Indagationes Mathematicae, Volume 31 (2020) no. 2, p. 277 | DOI:10.1016/j.indag.2020.01.005
- Discrete Magnetic Bottles on Quasi-Linear Graphs, Complex Analysis and Operator Theory, Volume 13 (2019) no. 3, p. 1401 | DOI:10.1007/s11785-018-00883-x
- Boundary representation of Dirichlet forms on discrete spaces, Journal de Mathématiques Pures et Appliquées, Volume 126 (2019), p. 109 | DOI:10.1016/j.matpur.2018.10.005
- The Adjacency Matrix and the Discrete Laplacian Acting on Forms, Mathematical Physics, Analysis and Geometry, Volume 22 (2019) no. 1 | DOI:10.1007/s11040-019-9301-0
- The Discrete Laplacian of a 2-Simplicial Complex, Potential Analysis, Volume 49 (2018) no. 2, p. 331 | DOI:10.1007/s11118-017-9659-1
- On the Eigenvalues of Weighted Directed Graphs, Complex Analysis and Operator Theory, Volume 11 (2017) no. 6, p. 1387 | DOI:10.1007/s11785-016-0615-7
- Spectral and scattering theory for Gauss–Bonnet operators on perturbed topological crystals, Journal of Mathematical Analysis and Applications, Volume 452 (2017) no. 2, p. 792 | DOI:10.1016/j.jmaa.2017.03.002
- The Gauss-Bonnet operator of an infinite graph, Analysis and Mathematical Physics, Volume 5 (2015) no. 2, p. 137 | DOI:10.1007/s13324-014-0090-0
- Graphs of finite measure, Journal de Mathématiques Pures et Appliquées, Volume 103 (2015) no. 5, p. 1093 | DOI:10.1016/j.matpur.2014.10.006
- Time regularity and long-time behavior of parabolic p-Laplace equations on infinite graphs, Journal of Differential Equations, Volume 259 (2015) no. 11, p. 6162 | DOI:10.1016/j.jde.2015.07.018
- Self-Adjoint Extensions of Discrete Magnetic Schrödinger Operators, Annales Henri Poincaré, Volume 15 (2014) no. 5, p. 917 | DOI:10.1007/s00023-013-0261-9
- Hardy inequality and asymptotic eigenvalue distribution for discrete Laplacians, Journal of Functional Analysis, Volume 266 (2014) no. 5, p. 2662 | DOI:10.1016/j.jfa.2013.10.012
- Operators on Networks, Semigroup Methods for Evolution Equations on Networks (2014), p. 11 | DOI:10.1007/978-3-319-04621-1_2
- Operator Semigroups, Semigroup Methods for Evolution Equations on Networks (2014), p. 77 | DOI:10.1007/978-3-319-04621-1_4
- A Spectral Property of Discrete Schrödinger Operators with Non-Negative Potentials, Integral Equations and Operator Theory, Volume 76 (2013) no. 2, p. 285 | DOI:10.1007/s00020-013-2060-6
- A note on self-adjoint extensions of the Laplacian on weighted graphs, Journal of Functional Analysis, Volume 265 (2013) no. 8, p. 1556 | DOI:10.1016/j.jfa.2013.06.004
- A Sears-type self-adjointness result for discrete magnetic Schrödinger operators, Journal of Mathematical Analysis and Applications, Volume 396 (2012) no. 2, p. 801 | DOI:10.1016/j.jmaa.2012.07.028
- Essential self-adjointness for combinatorial Schrödinger operators III- Magnetic fields, Annales de la Faculté des sciences de Toulouse : Mathématiques, Volume 20 (2011) no. 3, p. 599 | DOI:10.5802/afst.1319
- Essential Self-adjointness of Magnetic Schrödinger Operators on Locally Finite Graphs, Integral Equations and Operator Theory, Volume 71 (2011) no. 1, p. 13 | DOI:10.1007/s00020-011-1882-3
- Essential Self-adjointness for Combinatorial Schrödinger Operators II-Metrically non Complete Graphs, Mathematical Physics, Analysis and Geometry, Volume 14 (2011) no. 1, p. 21 | DOI:10.1007/s11040-010-9086-7
Cité par 27 documents. Sources : Crossref