A monotonicity property involving 3F2 and comparisons of the classical approximations of elliptical arc length, Handbook of Mathematical Functions. Dover SIAM J. Math. Anal, issue.1, pp.32-403, 1963. ,
Uniform Approximation and Explicit Estimates for the Prolate Spheroidal Wave Functions, Constructive Approximation, vol.17, issue.270, pp.15-45, 2016. ,
DOI : 10.1007/BF00282438
URL : https://hal.archives-ouvertes.fr/hal-01202320
Spectral decay of time and frequency limiting operator, Applied and Computational Harmonic Analysis, vol.42, issue.1, pp.1-20, 2017. ,
DOI : 10.1016/j.acha.2015.05.003
URL : https://hal.archives-ouvertes.fr/hal-01146395
Asymptotic behavior of spacing distributions for the eigenvalues of random matrices, Journal of Mathematical Physics, vol.14, issue.11, pp.14-1648, 1973. ,
DOI : 10.1063/1.1665903
On the Order Derivatives of Bessel Functions, Constructive Approximation, vol.37, issue.7???8, pp.47-68, 2017. ,
DOI : 10.1002/sapm195837175
Statistical Theory of the Energy Levels of Complex Systems. I, Journal of Mathematical Physics, vol.35, issue.1, pp.140-156, 1962. ,
DOI : 10.1002/j.1538-7305.1948.tb01338.x
On the eigenvalues of an integral equation arising in the theory of band-limited signals, Journal of Mathematical Analysis and Applications, vol.9, issue.3, pp.317-330, 1964. ,
DOI : 10.1016/0022-247X(64)90017-4
Tikhonov Wiener's problem for positive definite functions Available at https://doi.org/10, pp.209-226, 1007. ,
DOI : 10.1007/s00209-017-1978-9
URL : http://arxiv.org/pdf/1604.01302
Duration and Bandwidth Limiting: Prolate Functions, Sampling, and Applications . Applied and Numerical Harmonic Analysis Series, 2013. ,
DOI : 10.1007/978-0-8176-8307-8
The Eigenvalues Distribution of Time-Frequency Localization Operators. Available from arXiv ,
The approximation of almost time- and band-limited functions by their expansion in some orthogonal polynomials bases, Journal of Approximation Theory, vol.212, pp.41-65, 2016. ,
DOI : 10.1016/j.jat.2016.08.002
URL : https://hal.archives-ouvertes.fr/hal-01103588
On eigen-functions of an integral equation Mathematical problems in the theory of wave propagation, pp.66-150, 1970. ,
The eigenvalue behavior of certain convolution equations, Transactions of the American Mathematical Society, vol.115, pp.242-256, 1965. ,
DOI : 10.1090/S0002-9947-1965-0199745-4
On the density of phase-space expansions, IEEE Transactions on Information Theory, vol.39, issue.4, pp.1152-1156, 1993. ,
DOI : 10.1109/18.243434
Prolate sphero¨?dalsphero¨?dal wave functions, Fourier analysis and uncertainty II. Bell System Tech, J, vol.40, pp.65-84, 1961. ,
DOI : 10.1002/j.1538-7305.1961.tb03977.x
Prolate sphero¨?dalsphero¨?dal wave functions, Fourier analysis and uncertainty III: The dimension of the space of essentially time-and band limited signals, Bell System Tech. J, pp.41-1295, 1962. ,
Eigenvalue distribution of time and frequency limiting, Journal of Mathematical Analysis and Applications, vol.77, issue.2, pp.469-481, 1980. ,
DOI : 10.1016/0022-247X(80)90241-3
Random matrices, Pure and Applied Mathematics, vol.142, 2004. ,
Complete Version of Turan???s Lemma for Trigonometric Polynomials on the Unit Circumference, Operator Theory: Advances and Applications, pp.239-246, 2000. ,
DOI : 10.1007/978-3-0348-8378-8_20
NIST Handbook of Mathematical Functions, 2010. ,
Certain upper bounds on the eigenvalues associated with prolate spheroidal wave functions, Applied and Computational Harmonic Analysis, vol.35, issue.2, pp.309-340, 2013. ,
DOI : 10.1016/j.acha.2013.03.002
Prolate spheroidal wave functions, Fourier analysis and uncertainty I, Bell System Tech, J, vol.40, pp.43-64, 1961. ,
DOI : 10.1002/j.1538-7305.1961.tb03976.x
Some Asymptotic Expansions for Prolate Spheroidal Wave Functions, Journal of Mathematics and Physics, vol.43, issue.1-4, pp.99-140, 1965. ,
DOI : 10.1002/j.1538-7305.1964.tb01037.x
Degrees of Freedom of a Communication Channel: Using DOF Singular Values, IEEE Transactions on Information Theory, vol.56, issue.4, pp.1560-1573, 2010. ,
DOI : 10.1109/TIT.2010.2040895
Random matrices ,
DOI : 10.1090/gsm/132/02
A Review of Prolate Spheroidal Wave Functions from the Perspective of Spectral Methods, Journal of Mathematical Study, vol.50, issue.2, pp.101-143, 2017. ,
DOI : 10.4208/jms.v50n2.17.01
Asymptotic behavior of the eigenvalues of certain integral equations, II. Arc. Rational Mech. Anal, vol.17, pp.215-229, 1964. ,
Prolate spheroidal wavefunctions, quadrature and interpolation, Inverse Problems, vol.17, issue.4, pp.805-838, 2001. ,
DOI : 10.1088/0266-5611/17/4/315
E-mail address: Philippe.Jaming@math.u-bordeaux.fr A ,