A. Abdelmoula, M. Moakher, and B. Philippe, Localized spectral analysis for an inverse problem in geodesy, 2008.

A. Albertella, F. Anso, and N. Neeuw, Band-limited functions on a bounded spherical domain: the Slepian problem on the sphere, Journal of Geodesy, vol.73, issue.9, pp.73-436, 1999.
DOI : 10.1007/PL00003999

B. Atfeh, L. Baratchart, J. Leblond, and J. Partington, Bounded extremal and Cauchy-Laplace problems on the sphere and shell, The Journal of Fourier Analysis and Applications, pp.177-203, 2010.

L. Baratchart, A. B. Abda, F. B. Hassen, and J. Leblond, Recovery of pointwise sources or small inclusions in 2D domains and rational approximation, Inverse problems, pp.51-74, 2005.
DOI : 10.1088/0266-5611/21/1/005

L. Baratchart, D. Hardin, E. Lima, E. Saff, and B. Weiss, Inverse magnetization problems for a two-dimensional slab and generalizations of hodge decompositions, V Bell Syst, Tech. J, 2011.

L. Baratchart, J. Leblond, and J. Marmorat, Inverse source problem in a 3D ball from best meromorphic approximation on 2D slices, ETNA, pp.25-41, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00504716

L. Baratchart and M. Yattselev, Meromorphic approximants to complex Cauchy transforms with polar singularities Asymptotic formulas for the voltage potential in a composite medium containing close or touching disks of small diameter, Mat. Sb. Multiscale Model. Simul, vol.200, issue.4, pp.3-40, 2005.

A. Bultheel and B. D. Moor, Rational approximation in linear systems and control, Journal of Computational and Applied Mathematics, vol.121, issue.1-2, pp.355-378, 2000.
DOI : 10.1016/S0377-0427(00)00339-3

F. Chambat and Y. Ricard, Empirical 3-D basis for the internal density of a planet, Geophysical Journal International, vol.162, issue.1, pp.32-35, 2005.
DOI : 10.1111/j.1365-246X.2005.02650.x

URL : https://hal.archives-ouvertes.fr/hal-00093156

A. Chambodut, I. Panet, M. Mandea, D. Diament, M. Holschneider et al., Wavelet frames: an alternative to spherical harmonic representation of potential fields, Geophysical Journal International, vol.163, issue.3, pp.857-899, 2005.
DOI : 10.1111/j.1365-246X.2005.02754.x

G. Chen and J. Zhou, Boundary element methods, 1992.

M. Chung, K. Dalton, A. Evans, and R. Davidson, Tensor-Based Cortical Surface Morphometry via Weighted Spherical Harmonic Representation, IEEE Transactions on Medical Imaging, vol.27, issue.8, 2007.
DOI : 10.1109/TMI.2008.918338

S. Claessens, W. Featherstone, and F. Barthelmes, Experiences with point-mass gravity field modelling in the Perth region, Geomatics Research Australasia, pp.75-53, 2001.

M. Clerc, J. Leblond, J. Marmorat, and T. Papadopoulo, Source localization using rational approximation on plane sections, Inverse Problems, vol.28, issue.5, 2011.
DOI : 10.1088/0266-5611/28/5/055018

URL : https://hal.archives-ouvertes.fr/inria-00613644

B. Cuffin, A method for localizing EEG sources in realistic head models, IEEE Transactions on Biomedical Engineering, vol.42, issue.1, pp.68-71, 1995.
DOI : 10.1109/10.362917

P. Davis and P. Rabinowitz, Methods of Numerical Integration, 1984.

A. Badia, Summary of some results on an EEG inverse problem, Neurology and Clinical Neurophysiology, vol.104, 2004.

A. Badia and T. Duong, An inverse source problem in potential analysis, Inverse Problems, vol.16, issue.3, pp.651-663, 2000.
DOI : 10.1088/0266-5611/16/3/308

A. Badia and M. Farah, A stable recovering of dipole sources from partial boundary measurements, Inverse Problems, p.26, 2010.

A. Friedman and M. Vogelius, Identification of small inhomogeneities of extreme conductivity by boundary measurements: a theorem on continuous dependence, Archive for Rational Mechanics and Analysis, vol.34, issue.4, pp.299-326, 1989.
DOI : 10.1007/BF00281494

E. Gilbert and D. Slepian, Existence and generic properties of l 2 approximants of linear systems, IMA Journal of Mathematical Control and Information, vol.3, pp.89-101, 1986.

K. Gorski, E. Hivon, A. Banday, B. Wandelt, F. Hansen et al., HEALPix: A Framework for High???Resolution Discretization and Fast Analysis of Data Distributed on the Sphere, The Astrophysical Journal, vol.622, issue.2, pp.622-759, 2005.
DOI : 10.1086/427976

R. Gregory, Uniform bounds for P m n (cos ?) and the absolute convergence of series expansions in spherical surface harmonics, Quartely Journal of Mechanics and Applied Mathematics, pp.50-467, 1997.

V. Isakov, Inverse problems for partial differential equations, 1998.

K. Jerbi, J. Mosher, S. Baillet, and R. Leahy, On MEG forward modelling using multipolar expansions, Physics in Medicine and Biology, vol.47, issue.4, pp.47-523, 2002.
DOI : 10.1088/0031-9155/47/4/301

A. Karoui, Recent developments in fractals and related fields. Based on the international conference on fractals and related fields, Uncertainty principles, prolate spheroidal wave functions, and applications, 2010.

A. Karoui, J. Leblond, and A. Nicu, Slepian functions on the sphere with applications to signal recovery and inverse source problems, in preparation, 2012.

J. Keiner and D. Potts, Fast evaluation of quadrature formulae on the sphere, Mathematics of Computation, vol.77, issue.261, pp.397-419, 2008.
DOI : 10.1090/S0025-5718-07-02029-7

H. Landau and H. Pollak, Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - II, Bell System Technical Journal, vol.40, issue.1, pp.65-84, 1961.
DOI : 10.1002/j.1538-7305.1961.tb03977.x

J. Marmorat and M. Olivi, The RARL2 software: Realizations and Rational Approximation in L 2 -norm, url: http://wwwsop .inria.fr/apics, p.2

V. Michel, Regularized wavelet-based multiresolution recovery of the harmonic mass density distribution from data of the Earth's gravitational field at satellite height, Inverse problems, 2005.
DOI : 10.1088/0266-5611/21/3/013

V. Michel and A. Fokas, A unified approach to various techniques for the non-uniqueness of the inverse gravimetric problem and wavelet-based methods, Inverse Problems, vol.24, issue.4, p.24, 2008.
DOI : 10.1088/0266-5611/24/4/045019

L. Miranian, Slepian functions on the sphere, generalized Gaussian quadrature rule, Inverse Problems, vol.20, issue.3, 2004.
DOI : 10.1088/0266-5611/20/3/014

J. Mosher, P. Lewis, and R. Leahy, Multiple dipole modeling and localization from spatio-temporal MEG data, IEEE Transactions on Biomedical Engineering, vol.39, issue.6, pp.541-553, 1992.
DOI : 10.1109/10.141192

A. Nikiforov, Special functions of mathematical physics, 1988.
DOI : 10.1007/978-1-4757-1595-8

H. Ouerghi, Localization des sources ponctuelle dans une boule par approximation sur les sections planes: calcules des moments, Master's thesis, 2008.

W. Rudin, Analyse réelle et complexe, 1975.

J. Sarvas, Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem, Physics in Medicine and Biology, vol.32, issue.1, pp.11-12, 1987.
DOI : 10.1088/0031-9155/32/1/004

F. Simons and F. Dahlen, Spherical Slepian functions and the polar gap in geodesy, Geophysical Journal International, vol.166, issue.3, pp.1039-1061, 2006.
DOI : 10.1111/j.1365-246X.2006.03065.x

F. Simons, F. Dahlen, and M. Wieczorek, Spatiospectral Concentration on a Sphere, SIAM Review, vol.48, issue.3, pp.48-504, 2006.
DOI : 10.1137/S0036144504445765

D. Slepian, Prolate spheroidal wave functions, fourier analysis and uncertainty , V Bell Syst, Tech. J, vol.57, pp.1371-430, 1978.

I. Sloan and R. Womersley, Good approximation on the sphere, with application to geodesy and the scattering of sound, Journal of Computational and Applied Mathematics, vol.149, issue.1, pp.227-237, 2002.
DOI : 10.1016/S0377-0427(02)00532-0

N. Sneeuw and M. Van-gelderen, The polar gap, pp.559-568, 1997.
DOI : 10.1007/BFb0011717

D. Stromeyer and L. Ballani, Uniqueness of the inverse gravimetric problem for point mass models, Manuscr. Geodaet, vol.9, pp.125-136, 1984.

G. Szegö, Orthogonal polynomials, 1959.
DOI : 10.1090/coll/023

S. Vessella, Locations and strengths of point sources: stability estimates, Inverse Problems, vol.8, issue.6, pp.911-917, 1992.
DOI : 10.1088/0266-5611/8/6/008

B. Wellenhof and H. Moritz, Physical geodesy, 2006.

N. Young, An introduction to Hilbert space, 1998.
DOI : 10.1017/CBO9781139172011