M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, American Journal of Physics, vol.34, issue.2, 1972.
DOI : 10.1119/1.1972842

G. E. Andrews, R. Askey, and R. Roy, Special Functions, 2000.

A. Bonami and A. Karoui, Uniform bounds of prolate spheroidal wave functions and eigenvalues decay, Comptes Rendus Mathematique, vol.352, issue.3, pp.352-229234, 2014.
DOI : 10.1016/j.crma.2014.01.004

URL : https://hal.archives-ouvertes.fr/hal-01146376

A. Bonami and A. Karoui, Spectral decay of time and frequency limiting operator, Applied and Computational Harmonic Analysis, vol.42, issue.1, 2015.
DOI : 10.1016/j.acha.2015.05.003

URL : https://hal.archives-ouvertes.fr/hal-01202314

J. P. Boyd, Prolate spheroidal wave functions as an alternative to Chebyshev and Legendre polynomials for spectral element and pseudo-spectral algorithms, J. Comput. Phys, p.688716, 2004.
DOI : 10.1016/j.jcp.2004.03.010

J. P. Boyd, Approximation of an analytic function on a nite real interval by a bandlimited function and conjectures on properties of prolate spheroidal functions, Appl. Comput. Harmon. Anal, vol.25, issue.2, p.168176, 2003.

R. E. Dickinson, ON THE EXACT AND APPROXIMATE LINEAR THEORY OF VERTICALLY PROPAGATING PLANETARY ROSSBY WAVES FORCED AT A SPHERICAL LOWER BOUNDARY, Monthly Weather Review, vol.96, issue.7, p.405415, 1968.
DOI : 10.1175/1520-0493(1968)096<0405:OTEAAL>2.0.CO;2

Y. M. Dunster, Uniform Asymptotic Expansions for Prolate Spheroidal Functions with Large Parameters, SIAM Journal on Mathematical Analysis, vol.17, issue.6, p.14951524, 1986.
DOI : 10.1137/0517108

L. Gatteschi, Limitazione degli errori nelle formule asintotiche per le funzioni speciali. (Italian) Univ. e Politec, Torino. Rend. Sem. Mat, vol.16, p.8394, 1957.

M. L. Glasser and M. S. Klamkin, Some integrals of squares of Bessel functions, pp.12-315316, 1977.

L. Gosse, Compressed sensing with preconditioning for sparse recovery with subsampled matrices of Slepian prolate functions, ANNALI DELL'UNIVERSITA' DI FERRARA, vol.135, issue.1, pp.59-81116, 2013.
DOI : 10.1007/s11565-012-0159-3

URL : https://hal.archives-ouvertes.fr/hal-00560962

J. A. Hogan and J. D. Lakey, Duration and Bandwidth Limiting: Prolate Functions, Sampling, and Applications, Applied and Numerical Harmonic Analysis Series, 2013.
DOI : 10.1007/978-0-8176-8307-8

A. Karoui and T. Moumni, New ecient methods of computing the prolate spheroidal wave functions and their corresponding eigenvalues, Appl. Comput. Harmon. Anal, vol.24, issue.3, p.269289, 2008.

H. J. Landau and H. O. Pollak, Prolate spheroidal wave functions, Fourier analysis and uncertainty-III. The dimension of space of essentially time-and band-limited signals, Bell System Tech, J, pp.41-12951336, 1962.
DOI : 10.1002/j.1538-7305.1961.tb03977.x

H. J. Landau and H. Widom, Eigenvalue distribution of time and frequency limiting, Journal of Mathematical Analysis and Applications, vol.77, issue.2, p.469481, 1980.
DOI : 10.1016/0022-247X(80)90241-3

W. Lin, N. Kovvali, and L. Carin, Pseudospectral method based on prolate spheroidal wave functions for semiconductor nanodevice simulation, Computer Physics Communications, vol.175, issue.2, pp.175-7885, 2006.
DOI : 10.1016/j.cpc.2006.02.006

J. W. Miles, Asymptotic Approximations for Prolate Spheroidal Wave Functions, Studies in Applied Mathematics, vol.49, issue.4, p.315349, 1975.
DOI : 10.1002/sapm1975544315

J. W. Miles, Asymptotic Eigensolutions of Laplace's Tidal Equation, Proc. R. Soc. Lond. A, p.377400, 1977.
DOI : 10.1098/rspa.1977.0040

R. Müller, On the Structure of the Global Linearized Primitive Equations Part II: Laplace's Tidal Equations, Beitr. Phys. Atmosph, vol.62, issue.2, p.112125, 1989.

R. Müller, Stable and unstable eigensolutions of laplace???s tidal equations for zonal wavenumber zero, Advances in Atmospheric Sciences, vol.62, issue.1, p.2140, 1993.
DOI : 10.1007/BF02656951

A. N. Nikoforov and V. B. Uvarov, Special functions of mathematical physics, translated from the Russian edition, 1988.

C. Niven, On the Conduction of Heat in Ellipsoids of Revolution, Philosophical Transactions of the Royal Society of London, vol.171, issue.0, pp.117-151, 1880.
DOI : 10.1098/rstl.1880.0005

W. P. Oconnor, On the Application of the Spheroidal Wave Equation to the Dynamical Theory of the Long-Period Zonal Tides in a Global Ocean, Proc. R. Soc. Lond. A, p.189196, 1905.
DOI : 10.1098/rspa.1992.0143

F. W. Olver, Asymptotics and Special Functions, 1974.

A. Osipov, Certain inequalities involving prolate spheroidal wave functions and associated quantities, Applied and Computational Harmonic Analysis, vol.35, issue.3, p.359393, 2013.
DOI : 10.1016/j.acha.2012.10.002

URL : http://arxiv.org/abs/1206.4056

D. Slepian and H. O. Pollak, Prolate spheroidal wave functions, Fourier analysis and uncertaintyI , Bell System Tech, J, vol.40, p.4364, 1961.
DOI : 10.1002/j.1538-7305.1961.tb03976.x

D. Slepian, Prolate spheroidal wave functions, Fourier analysis and uncertaintyIV: Extensions to many dimensions; generalized prolate spheroidal functions, Bell System Tech, J, pp.43-30093057, 1964.

D. Slepian, Some Asymptotic Expansions for Prolate Spheroidal Wave Functions, Journal of Mathematics and Physics, vol.43, issue.1-4, p.99140, 1965.
DOI : 10.1002/sapm196544199

H. Xiao, V. Rokhlin, and N. Yarvin, Prolate spheroidal wave functions, quadrature and interpolation, Inverse Problems, vol.17, p.805838, 2001.

G. Walter and T. Soleski, A new friendly method of computing prolate spheroidal wave functions and wavelets, Applied and Computational Harmonic Analysis, vol.19, issue.3, p.432443, 2005.
DOI : 10.1016/j.acha.2005.04.001

L. L. Wang, Analysis of spectral approximations using prolate spheroidal wave functions, Mathematics of Computation, vol.79, issue.270, p.807827, 2010.
DOI : 10.1090/S0025-5718-09-02268-6

G. N. Watson, A Treatise on the Theory of Bessel Functions, Second Edition, 1966.

H. Widom, Asymptotic behavior of the eigenvalues of certain integral equations. II, Archive for Rational Mechanics and Analysis, p.215229, 1964.