S. Agmon and L. Hörmander, Asymptotic properties of solutions of differential equations with simple characteristics, Journal d'Analyse Math??matique, vol.53, issue.2, pp.1-38, 1976.
DOI : 10.1007/BF02786703

S. Agmon, B. F. Jones, J. With, G. W. Batten, and J. , Lectures on elliptic boundary value problems Prepared for publication, Van Nostrand Mathematical Studies, issue.2, 1965.

E. F. Beckenbach and R. Bellman, Inequalities. Second revised printing, Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge, 1965.

B. Colbois, A. Soufi, and A. Savo, Eigenvalues of the Laplacian on a compact manifold with density, Communications in Analysis and Geometry, vol.23, issue.3, pp.639-670, 2015.
DOI : 10.4310/CAG.2015.v23.n3.a6

URL : https://hal.archives-ouvertes.fr/hal-00870126

D. E. Edmunds and W. D. Evans, Spectral theory and differential operators. Oxford Mathematical Monographs, 1987.

A. Soufi and S. Ilias, Majoration de la seconde valeur propre d'un op??rateur de Schr??dinger sur une vari??t?? compacte et applications, Journal of Functional Analysis, vol.103, issue.2, pp.294-316, 1992.
DOI : 10.1016/0022-1236(92)90123-Z

A. Soufi and S. Ilias, Second Eigenvalue of Schr???dinger Operators???and Mean Curvature, Communications in Mathematical Physics, vol.208, issue.3, pp.761-770, 2000.
DOI : 10.1007/s002200050009

S. Gallot, Inégalités isopérimétriques et analytiques sur les variétés riemanniennes Astérisque On the geometry of differentiable manifolds, pp.163-1645, 1986.

A. Grigor, ?. Yan, Y. Netrusov, and S. Yau, Eigenvalues of elliptic operators and geometric applications, Surveys in differential geometry, pp.147-217, 2004.

E. M. Harrell, I. , and J. Stubbe, On sums of graph eigenvalues, Linear Algebra and its Applications, vol.455, pp.168-186, 2014.
DOI : 10.1016/j.laa.2014.05.001

A. Hassannezhad, Eigenvalues of perturbed Laplace operators on compact manifolds, Pacific Journal of Mathematics, vol.264, issue.2, pp.333-354, 2013.
DOI : 10.2140/pjm.2013.264.333

R. Hempel, L. A. Seco, and B. Simon, The essential spectrum of Neumann Laplacians on some bounded singular domains, Journal of Functional Analysis, vol.102, issue.2, pp.448-483, 1991.
DOI : 10.1016/0022-1236(91)90130-W

C. E. Heil and D. F. Walnut, Continuous and Discrete Wavelet Transforms, SIAM Review, vol.31, issue.4, pp.628-666, 1989.
DOI : 10.1137/1031129

L. Hörmander, The analysis of linear partial differential operators. I, volume 256 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 1983.

P. Kröger, Upper bounds for the Neumann eigenvalues on a bounded domain in euclidean space, Journal of Functional Analysis, vol.106, issue.2, pp.353-357, 1992.
DOI : 10.1016/0022-1236(92)90052-K

A. Laptev, Dirichlet and Neumann Eigenvalue Problems on Domains in Euclidean Spaces, Journal of Functional Analysis, vol.151, issue.2, pp.531-545, 1992.
DOI : 10.1006/jfan.1997.3155

A. Laptev, Recent improvements of Berezin?Li & Yau type inequalities 2013 BIRS lecture available at http://www.birs.ca/workshops Sums of Laplace eigenvalues?rotationally symmetric maximizers in the plane, J. Funct. Anal, vol.260, issue.6, pp.1795-1823, 2011.

L. Li and L. , Tang Some upper bounds for sums of eigenvalues of the Neumann Laplacian, Proc. Amer, pp.3301-3307, 2006.

E. H. Lieb, Coherent States as a Tool for Obtaining Rigorous Bounds Coherent states: Past, present, and future, Proceedings, Oak Ridge, pp.267-278, 1994.

E. H. Lieb and J. P. Solovej, Quantum coherent operators: A generalization of coherent states, Letters in Mathematical Physics, vol.12, issue.5, pp.145-154, 1991.
DOI : 10.1007/BF00405179

H. L. Montgomery, Minimal theta functions, Glasgow Mathematical Journal, vol.175, issue.01, pp.75-85, 1988.
DOI : 10.1017/S0305004100038330

M. Reed and B. Simon, Methods of modern mathematical physics. IV. Analysis of operators, 1978.

R. S. Strichartz, Fourier asymptotics of fractal measures, Journal of Functional Analysis, vol.89, issue.1, pp.154-187, 1990.
DOI : 10.1016/0022-1236(90)90009-A

R. S. Strichartz, Estimates for Sums of Eigenvalues for Domains in Homogeneous Spaces, Journal of Functional Analysis, vol.137, issue.1, pp.152-190, 1996.
DOI : 10.1006/jfan.1996.0043

W. Thirring, Quantum mathematical physics Atoms, molecules and large systems, Translated from the, 1979.

J. Weidmann, Linear operators in Hilbert spaces, volume 68 of Graduate Texts in Mathematics, 1980.