B. D. Coleman and V. J. Mizel, Norms and semi-groups in the theory of fading memory, Archive for Rational Mechanics and Analysis, vol.23, issue.2, pp.87-123, 1966.
DOI : 10.1007/BF00251727

D. Masi, A. Galves, A. Löcherbach, E. Presutti, and E. , Hydrodynamic Limit for Interacting Neurons, Journal of Statistical Physics, vol.11, issue.3, pp.866-902, 2015.
DOI : 10.1007/s10955-014-1145-1

K. Engel, R. Nagel, and R. Schnaubelt, One-parameter semigroups for linear evolution equations of Graduate Texts in Mathematics, 2000.

N. Fournier and E. Löcherbach, On a toy model of interacting neurons, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.52, issue.4, 2014.
DOI : 10.1214/15-AIHP701

I. Fredholm, Sur une classe d?????quations fonctionnelles, Acta Mathematica, vol.27, issue.0, pp.365-390, 1903.
DOI : 10.1007/BF02421317

W. Gerstner and W. M. Kistler, Spiking neuron models, 2002.
DOI : 10.1017/cbo9780511815706

M. P. Gualdani, S. Mischler, and C. Mouthot, Factorization of non-symmetric operators and exponential H-Theorem, 2010.

T. Kato, Perturbation theory for linear operators, Classics in Mathematics, 1995.
DOI : 10.1007/978-3-662-12678-3

S. Mischler and . Erratum, Spectral analysis of semigroups and growthfragmentation equations
URL : https://hal.archives-ouvertes.fr/hal-01422273

S. Mischler, Semigroups in Banach spaces -splitting approach for spectral analysis and asymptotics estimates

S. Mischler and C. Mouhot, Stability, Convergence to Self-Similarity and Elastic Limit for the Boltzmann Equation for Inelastic Hard Spheres, Communications in Mathematical Physics, vol.26, issue.2???4, pp.431-502, 2009.
DOI : 10.1007/s00220-009-0773-9
URL : https://hal.archives-ouvertes.fr/hal-00124876

S. Mischler, C. Quiñinao, and J. Touboul, On a Kinetic Fitzhugh???Nagumo Model of Neuronal Network, Communications in Mathematical Physics, vol.13, issue.2, pp.1001-1042, 2016.
DOI : 10.1007/s00220-015-2556-9
URL : https://hal.archives-ouvertes.fr/hal-01108872

S. Mischler and J. Scher, Spectral analysis of semigroups and growth-fragmentation equations, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.33, issue.3, pp.849-898, 2016.
DOI : 10.1016/j.anihpc.2015.01.007
URL : https://hal.archives-ouvertes.fr/hal-01422273

S. Mischler and I. Tristani, Analyse spectrale uniforme des ??quations de Fokker-Planck discr??te, fractionnaire et classique, Journal de l?????cole polytechnique ??? Math??matiques, vol.4, p.1177101, 2015.
DOI : 10.5802/jep.46

K. Pakdaman, B. Perthame, and D. Salort, Dynamics of a structured neuron population, Nonlinearity, vol.23, issue.1, pp.55-75, 2010.
DOI : 10.1088/0951-7715/23/1/003
URL : https://hal.archives-ouvertes.fr/hal-00387413

K. Pakdaman, B. Perthame, and D. Salort, Relaxation and Self-Sustained Oscillations in the Time Elapsed Neuron Network Model, SIAM Journal on Applied Mathematics, vol.73, issue.3, pp.1260-1279, 2013.
DOI : 10.1137/110847962

K. Pakdaman, B. Perthame, and D. Salort, Adaptation and Fatigue Model for Neuron Networks and Large Time Asymptotics in a Nonlinear Fragmentation Equation, The Journal of Mathematical Neuroscience, vol.4, issue.1, pp.14-26, 2014.
DOI : 10.1016/j.jmaa.2005.12.036
URL : https://hal.archives-ouvertes.fr/hal-01054561

A. Pazy, Semigroups of linear operators and applications to partial differential equations, of Applied Mathematical Sciences, 1983.
DOI : 10.1007/978-1-4612-5561-1

C. Quiñinao, A microscopic spiking neuronal network for the agestructured model, p.1121061, 2015.

M. Ribari? and I. Vidav, Analytic properties of the inverse A(z)???1 of an analytic linear operator valued function A (z), Archive for Rational Mechanics and Analysis, vol.28, issue.4, pp.298-310, 1969.
DOI : 10.1007/BF00281506

P. Robert and J. D. Touboul, On the Dynamics of Random Neuronal Networks, Journal of Statistical Physics, vol.11, issue.1, 2014.
DOI : 10.1186/2190-8567-4-14
URL : https://hal.archives-ouvertes.fr/hal-01075242

I. Tristani, Boltzmann equation for granular media with thermal force in a weakly inhomogeneous setting, Journal of Functional Analysis, vol.270, issue.5, pp.1922-1970, 2016.
DOI : 10.1016/j.jfa.2015.09.025
URL : https://hal.archives-ouvertes.fr/hal-00906770

J. Voigt, A perturbation theorem for the essential spectral radius of strongly continuous semigroups, Monatshefte f???r Mathematik, vol.22, issue.2, pp.153-161, 1980.
DOI : 10.1007/BF01303264

V. Volterra, Theory of functionals and of integral and integrodifferential equations With a preface by G. C. Evans, a biography of Vito Volterra and a bibliography of his published works by E. Whittaker, 1959.

Q. Weng, General time elapsed neuron network model: well-posedness and strong connectivity regime, p.1243163, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01243163