M. B. Abrahamse, Toeplitz operators in multiply connected regions, Bulletin of the American Mathematical Society, vol.77, issue.3, pp.449-454, 1971.
DOI : 10.1090/S0002-9904-1971-12734-9

D. Alpay, L. Baratchart, and J. Leblond, Some extremal problems linked with identification from partial frequency data, 10th conference in Analysis and optimization of systems, LNCIS, vol.185, pp.563-573, 1992.

D. Alpay and J. Leblond, Traces of Hardy functions and reproducing kernel Hilbert spaces, Archiv der Mathematik, vol.13, issue.6, pp.490-499, 1995.
DOI : 10.1007/BF01195131

C. P. Aryana and K. F. Clancey, On the existence of eigenvalues of Toeplitz operators on planar regions, Proc. Amer, pp.3007-3018, 2004.

B. Atfeh, L. Baratchart, J. Leblond, and J. R. Partington, Bounded Extremal and Cauchy???Laplace Problems on??the??Sphere and Shell, Journal of Fourier Analysis and Applications, vol.11, issue.2, pp.177-203, 2010.
DOI : 10.1007/s00041-009-9110-0
URL : https://hal.archives-ouvertes.fr/hal-00798945

L. Baratchart, J. Grimm, J. Leblond, and J. R. Partington, Asymptotic Estimates for Interpolation and Constrained Approximation in $ H^{2} $ by Diagonalization of Toeplitz Operators, Integral Equations and Operator Theory, vol.45, issue.3, pp.269-299, 2003.
DOI : 10.1007/s000200300005

L. Baratchart and J. Leblond, Hardy Approximation to L p Functions on Subsets of the Circle with 1< =p< = infinity, Constructive Approximation, vol.14, issue.1, pp.41-56, 1998.
DOI : 10.1007/s003659900062

L. Baratchart, J. Leblond, and J. R. Partington, Hardy Approximation to $L^$ Functions on Subsets of the Circle, Constructive Approximation, vol.12, issue.3, pp.423-435, 1996.
DOI : 10.1007/s003659900022
URL : https://hal.archives-ouvertes.fr/inria-00074299

L. Baratchart, J. Leblond, J. R. Partington, and N. Torkhani, Robust identification from band-limited data, IEEE Transactions on Automatic Control, vol.42, issue.9, pp.1318-1325, 1997.
DOI : 10.1109/9.623101
URL : https://hal.archives-ouvertes.fr/inria-00074187

B. Beauzamy, Introduction to Banach spaces and their geometry, North- Holland Mathematics Studies 68, 1985.

A. Böttcher and B. Silbermann, Introduction to large truncated Toeplitz matrices, 1999.
DOI : 10.1007/978-1-4612-1426-7

H. Brézis, Analyse fonctionnelle, théorie et applications, 1999.

I. Chalendar and J. R. Partington, Approximation problems and representations of Hardy spaces in circular domains, Studia Math, vol.136, pp.255-269, 1999.

I. Chalendar and J. R. Partington, Constrained approximation and invariant subspaces, Journal of Mathematical Analysis and Applications, vol.280, issue.1, pp.176-187, 2003.
DOI : 10.1016/S0022-247X(03)00099-4
URL : http://doi.org/10.1016/s0022-247x(03)00099-4

I. Chalendar, J. R. Partington, and M. Smith, Approximation in reflexive Banach spaces and applications to the invariant subspace problem, Proceedings of the American Mathematical Society, vol.132, issue.04, pp.1133-1142, 2004.
DOI : 10.1090/S0002-9939-03-07152-1

P. G. Ciarlet, IntroductionàIntroductionà l'analyse numérique matricielle etàetà l'optimisation, 1982.

P. L. Duren, Theory of H p spaces, Pure and Applied Mathematics, vol.38, 1970.

Y. Fischer, Approximation dans des classes de fonctions analytiques généralisées et résolution deprobì emes inverses pour les tokamaks, 2011.

Y. Fischer, J. Leblond, J. R. Partington, and E. Sincich, Bounded extremal problems in Hardy spaces for the conjugate Beltrami equation in simply-connected domains, Applied and Computational Harmonic Analysis, vol.31, issue.2, pp.31-264, 2011.
DOI : 10.1016/j.acha.2011.01.003
URL : https://hal.archives-ouvertes.fr/inria-00460820

M. Jaoua, J. Leblond, M. Mahjoub, and J. R. Partington, Robust numerical algorithms based on analytic approximation for the solution of inverse problems in annular domains, IMA Journal of Applied Mathematics, vol.74, issue.4, pp.74-481, 2009.
DOI : 10.1093/imamat/hxn041
URL : https://hal.archives-ouvertes.fr/inria-00258512

J. Leblond, M. Mahjoub, and J. R. Partington, Analytic extensions and Cauchytype inverse problems on annular domains: stability results, J. Inverse Ill-Posed Probl, pp.189-204, 2006.

J. Leblond, J. Marmorat, and J. R. Partington, Analytic approximation with real constraints, with applications to inverse diffusion problems, J. Inverse Ill- Posed Probl, pp.89-105, 2008.

L. Miranian, Slepian functions on the sphere, generalized Gaussian quadrature rule, Inverse Problems, vol.20, issue.3, pp.877-892, 2004.
DOI : 10.1088/0266-5611/20/3/014

N. K. Nikolski, Operators, functions, and systems: an easy reading, Hardy, Hankel, and Toeplitz. Math. Surveys and Monographs 92, 2002.

C. Pommerenke, Boundary behaviour of conformal maps, 1992.
DOI : 10.1007/978-3-662-02770-7

M. Rosenblum and J. Rovnyak, Hardy classes and operator theory, 1997.

D. Sarason, The H p spaces of an annulus, Mem. Amer, Math. Soc, vol.56, 1965.

D. Sarason, Algebraic properties of truncated Toeplitz operators, Operators and Matrices, vol.1, issue.4, pp.491-526, 2007.
DOI : 10.7153/oam-01-29

F. J. Simons, F. A. Dahlen, and M. A. Wieczorek, Spatiospectral Concentration on a Sphere, SIAM Review, vol.48, issue.3, pp.504-536, 2006.
DOI : 10.1137/S0036144504445765

D. Slepian, Prolate spheroidal wave functions, Fourier analysis and uncertainty . V. The Discrete Case, Bell System Tech, J, vol.57, pp.1371-1430, 1978.
DOI : 10.1002/j.1538-7305.1961.tb03976.x

D. Slepian and H. O. Pollak, Prolate spheroidal wave functions, Fourier analysis and uncertainty. I, Bell System Tech, J, vol.40, pp.43-63, 1961.

M. Smith, The Spectral Theory of Toeplitz Operators Applied to Approximation Problems in Hilbert Spaces, Constructive Approximation, vol.22, issue.1, pp.47-65, 2005.
DOI : 10.1007/s00365-004-0591-4