Bibliography

Major publications by the team in recent years

• 1S. Amari, F. Seyfert, M. Bekheit.
  
  Theory of Coupled Resonator Microwave Bandpass Filters of Arbitrary Bandwidth, in: Microwave Theory and Techniques, IEEE Transactions on, August 2010, vol. 58, n^o 8, pp. 2188 -2203.
• 2B. Atfeh, L. Baratchart, J. Leblond, J. R. Partington.
  
  Bounded extremal and Cauchy-Laplace problems on the sphere and shell, in: J. Fourier Anal. Appl., 2010, vol. 16, n^o 2, pp. 177–203, Published online Nov. 2009.
  
  http://dx.doi.org/10.1007/s00041-009-9110-0
• 3L. Baratchart, J. Leblond, J.-P. Marmorat.
  
  Sources identification in 3D balls using meromorphic approximation in 2D disks, in: Electronic Transactions on Numerical Analysis (ETNA), 2006, vol. 25, pp. 41–53.
• 4L. Baratchart, J. Leblond, S. Rigat, E. Russ.
  
  Hardy spaces of the conjugate Beltrami equation, in: Journal of Functional Analysis, 2010, vol. 259, n^o 2, pp. 384-427.
  
  http://dx.doi.org/10.1016/j.jfa.2010.04.004
• 5L. Baratchart, F. Mandréa, E. B. Saff, F. Wielonsky.
  
  2D inverse problems for the Laplacian: a meromorphic approximation approach, in: Journal de Math. Pures et Appliquées, 2008, vol. 86, pp. 1-41.
• 6L. Baratchart, H. Stahl, M. Yattselev.
  
  Weighted Extremal Domains and Best Rational Approximation, in: Advances in Mathematics, 2012, vol. 229, pp. 357-407.
  
  http://hal.inria.fr/hal-00665834
• 7L. Baratchart, M. Yattselev.
  
  Padé approximants to certain elliptic-type functions, in: Jour. d'Analyse, 2013, vol. 121, n^o 1, pp. 31–86.
• 8R. Cameron, J.-C. Faugère, F. Rouillier, F. Seyfert.
  
  Exhaustive approach to the coupling matrix synthesis problem and application to the design of high degree asymmetric filters, in: International Journal of RF and Microwave Computer-Aided Engineering, 2007, vol. 17, n^o 1, pp. 4–12.
  
  http://hal.inria.fr/hal-00663777
• 9M. Clerc, J. Leblond, J.-P. Marmorat, T. Papadopoulo.
  
  Source localization using rational approximation on plane sections, in: Inverse Problems, May 2012, vol. 28, n^o 5, 24 p.
  
  http://hal.inria.fr/inria-00613644
• 10B. Hanzon, M. Olivi, R. L. Peeters.
  
  Balanced realizations of discrete-time stable all-pass systems and the tangential Schur algorithm, in: Linear Algebra and its Applications, 2006, vol. 418, pp. 793-820.
  
  http://dx.doi.org/10.1016/j.laa.2006.09.029
• 11V. Lunot, F. Seyfert, S. Bila, A. Nasser.
  
  Certified Computation of Optimal Multiband Filtering Functions, in: IEEE Transactions on Microwave Theory and Techniques, 2008, vol. 56, n^o 1, pp. 105-112.
  
  http://dx.doi.org/10.1109/TMTT.2007.912234
• 12J.-P. Marmorat, M. Olivi.
  
  Nudelman Interpolation, Parametrization of Lossless Functions and balanced realizations, in: Automatica, 2007, vol. 43, pp. 1329–1338.
  
  http://dx.doi.org/10.1016/j.automatica.2007.01.020
• 13M. Olivi, F. Seyfert, J.-P. Marmorat.
  
  Identification of microwave filters by analytic and rational H2 approximation, in: Automatica, January 2013, vol. 49, n^o 2, pp. 317-325. [ DOI : 10.1016/j.automatica.2012.10.005 ]
  
  http://hal.inria.fr/hal-00753824

Publications of the year

Articles in International Peer-Reviewed Journals

• 14L. Baratchart, Y. Fischer, J. Leblond.
  
  Dirichlet/Neumann problems and Hardy classes for the planar conductivity equation, in: Complex Variables and Elliptic Equations, 2014, 41 p. [ DOI : 10.1080/17476933.2012.755755 ]
  
  https://hal.archives-ouvertes.fr/hal-00909577
• 15H. Ezzeddine, K. Frigui, S. Bila, S. Verdeyme, F. Seyfert, J. Puech, L. Estagerie, D. Pacaud.
  
  Design and implementation of compact diplexers using dual-mode cavities, in: International Journal of RF and Microwave Computer Aided Engineering, 2014, forthcoming. [ DOI : 10.1002/mmce.20760 ]
  
  https://hal-unilim.archives-ouvertes.fr/hal-00924828
• 16J. Leblond.
  
  Identifiability Properties for Inverse Problems in EEG Data Processing and Medical Engineering with Observability and Optimization Issues, in: Acta Applicandae Mathematicae, 2014, 16 p, Proceedings of the Workshop on Control and Observation of Nonlinear Control Systems with Application to Medicine (CONCSAM, Hawaii, 2013). [ DOI : 10.1007/s10440-014-9951-7 ]
  
  https://hal.archives-ouvertes.fr/hal-00875006
• 17D. Pacaud, F. Seyfert, H. Ezzeddine, S. Verdeyme, S. Bila, J. Puech, L. Estagerie.
  
  Optimized Synthesis of Self-Equalized Microwave Filters, in: IEEE Transactions on Microwave Theory and Techniques, July 2014, vol. 62, n^o 8, 6 p. [ DOI : 10.1109/TMTT.2014.2332135 ]
  
  https://hal.inria.fr/hal-01096240

International Conferences with Proceedings

• 18L. Baratchart, M. Olivi, F. Seyfert.
  
  Generalized Nevanlinna-Pick interpolation on the boundary. Application to impedance matching, in: MTNS-21st Symposium on Mathematical Theory of Networks and Systems, Groninguen, Netherlands, July 2014.
  
  https://hal.inria.fr/hal-00920564
• 19F. Seyfert, M. Oldoni, M. Olivi, S. Lefteriu, D. Pacaud.
  
  Deembedding of filters in multiplexers via rational approximation and interpolation, in: IMS - IEEE International Microwave Symposium, Tampa Bay, Florida, United States, June 2014.
  
  https://hal.inria.fr/hal-01052718
• 20F. Seyfert.
  
  Synthesis of Microwave filters: a novel approach based on computer algebra, in: MTNS-21st Symposium on Mathematical Theory of Networks and Systems, Groningen, Netherlands, July 2014.
  
  https://hal.archives-ouvertes.fr/hal-01100790

Scientific Books (or Scientific Book chapters)

• 21M. Oldoni, G. Macchiarella, F. Seyfert.
  
  Synthesis and Modelling Techniques for Microwave Filters and Diplexers: Advances in Analytical Methods with Applications to Design and Tuning, Scholars’ Press, February 2014.
  
  https://hal.inria.fr/hal-01096252

Internal Reports

• 22L. Baratchart, L. Bourgeois, J. Leblond.
  
  Uniqueness results for 2D inverse Robin problems with bounded coefficient, Inria Sophia Antipolis ; Inria Saclay, January 2015, n^o RR-8665, Travail relié à la pré-publication du même titre, hal-01084428, November 2014. On présente ici les résultats dans un cadre plus simple et avec des preuves différentes.
  
  https://hal.inria.fr/hal-01104629
• 23L. Baratchart, S. Chevillard, F. Seyfert.
  
  On Transfer Functions Realizable with Active Electronic Components, Inria Sophia Antipolis, December 2014, n^o RR-8659, 36 p.
  
  https://hal.inria.fr/hal-01098616
• 24L. Baratchart, J. Leblond, D. Ponomarev.
  
  Constrained optimization in classes of analytic functions with prescribed pointwise values, January 2014, n^o RR-8459.
  
  https://hal.inria.fr/hal-00938491

Other Publications

• 25L. Baratchart, L. Bourgeois, J. Leblond.
  
  Uniqueness results for inverse Robin problems with bounded coefficient, November 2014.
  
  https://hal.inria.fr/hal-01084428
• 26L. Baratchart, S. Chevillard, T. Qian.
  
  Minimax principle and lower bounds in H${}^2$-rational approximation, January 2015, Submitted to the special issue of Journal of Approximation Theory / Matematicheskii Sbornik, to the memory of A. A. Gonchar and H. Stahl.
  
  https://hal.inria.fr/hal-00922815
• 27S. Chaabi, S. Rigat.
  
  Decomposition theorem and Riesz basis for axisymmetric potentials in the right half-plane, January 2014.
  
  https://hal.archives-ouvertes.fr/hal-00940237
• 28T. Jordanov, J.-P. Marmorat, M. Clerc, J. Leblond, A. waelkens, T. Papadopoulo.
  
  FindSources3D - Source Localization Using Rational Approximation on Plane Sections, Poster listings, June 2014, Organization Human Brain Mapping, Annual Meeting.
  
  https://hal.inria.fr/hal-01098108

References in notes

• 29N. I. Achieser.
  
  Elements of the Theory of Elliptic Functions, AMS, 1990.
• 30D. Alpay, L. Baratchart, A. Gombani.
  
  On the Differential Structure of Matrix-Valued Rational Inner Functions, in: Operator Theory : Advances and Applications, 1994, vol. 73, pp. 30–66.
• 31J. A. Ball, I. Gohberg, L. Rodman.
  
  Interpolation of rational matrix functions, Birkhäuser, 1990.
• 32L. Baratchart.
  
  A remark on uniqueness of best rational approximants of degree 1 in $L^2$ of the circle, in: Elec. Trans.on Numerical Anal., 2006, vol. 25, pp. 54–66.
• 33L. Baratchart.
  
  On the $H^2$ Rational Approximation of Markov Matrix-Valued Functions, in: Proc. 17th Symposium on Mathematical Theory of Networks and Systems (MTNS), Kyoto, Japon, 2006, pp. 180–182.
• 34L. Baratchart, A. Borichev, S. Chaabi.
  
  Pseudo-holomorphic functions at the critical exponent, September 2013, Submitted.
  
  http://hal.inria.fr/hal-00824224
• 35L. Baratchart, M. Cardelli, M. Olivi.
  
  Identification and rational $L^2$ approximation: a gradient algorithm, in: Automatica, 1991, vol. 27, pp. 413–418.
• 36L. Baratchart, M. Chyba, J.-B. Pomet.
  
  A Grobman-Hartman theorem for control systems, in: J. Dyn. Differential Eqs., 2007, vol. 19, pp. 75-107.
• 37L. Baratchart, L. Golinskii, S. Kupin.
  
  Orthogonal rational functions and nonstationary stochastic processes: a Szegő theory, in: Proc. 19th Symposium on Mathematical Theory of Networks and Systems, Budapest, 2010.
• 38L. Baratchart, D. Hardin, E. A. Lima, E. B. Saff, B. Weiss.
  
  Characterizing kernels of operators related to thin-plate magnetizations via generalizations of Hodge decompositions, in: Inverse Problems, 2013, vol. 29, n^o 1. [ DOI : 10.1088/0266-5611/29/1/015004 ]
  
  http://hal.inria.fr/hal-00919261
• 39L. Baratchart, R. Kuestner, V. Totik.
  
  Zero distributions via orthogonality, in: Annales de l'Institut Fourier, 2005, vol. 55, n^o 5, pp. 1455–1499.
• 40L. Baratchart, S. Kupin, V. Lunot, M. Olivi.
  
  Multipoint Schur algorithm and orthogonal rational functions: convergence properties, I, in: Journal d'Analyse, 2011, vol. 112, pp. 207-255.
  
  http://arxiv.org/abs/0812.2050v3
• 41L. Baratchart, J. Leblond.
  
  Silent electrical sources in domains of ${ℝ}^3$, In preparation.
• 42L. Baratchart, J. Leblond.
  
  Hardy approximation to $L^p$ functions on subsets of the circle with $1\le p<\infty$, in: Constructive Approximation, 1998, vol. 14, pp. 41–56.
• 43L. Baratchart, J. Leblond, F. Mandréa, E. B. Saff.
  
  How can meromorphic approximation help to solve some 2D inverse problems for the Laplacian?, in: Inverse Problems, 1999, vol. 15, n^o 1, pp. 79–90.
  
  http://dx.doi.org/10.1088/0266-5611/15/1/012
• 44L. Baratchart, J. Leblond, J. R. Partington.
  
  Hardy approximation to $L^{\infty }$ functions on subsets of the circle, in: Constructive Approximation, 1996, vol. 12, pp. 423–435.
• 45L. Baratchart, J. Leblond, F. Seyfert.
  
  Extremal problems of mixed type in $H^2$ of the circle, Inria, 2009, n^o RR-7087.
  
  http://fr.arxiv.org/abs/0911.1441
• 46L. Baratchart, F. Mandréa, E. B. Saff, F. Wielonsky.
  
  2D inverse problems for the Laplacian: a meromorphic approximation approach, in: Journal de Math. Pures et Appliquées, 2008, vol. 86, pp. 1-41.
• 47L. Baratchart, M. Olivi.
  
  Index of critical points in $l^2$-approximation, in: System and Control Letters, 1988, vol. 10, pp. 167–174.
• 48L. Baratchart, M. Olivi.
  
  Critical points and error rank in best $H^2$ matrix rational approximation of fixed McMillan degree, in: Constructive Approximation, 1998, vol. 14, pp. 273–300.
• 49L. Baratchart, E. B. Saff, F. Wielonsky.
  
  A criterion for uniqueness of a critical point in $H^2$ rational approximation, in: Journal d'Analyse, 1996, vol. 70, pp. 225–266.
• 50L. Baratchart, F. Seyfert.
  
  An $L^p$ analog to AAK theory for $p\ge 2$, in: Journal of Functional Analysis, 2002, vol. 191, n^o 1, pp. 52–122.
• 51L. Baratchart, H. Stahl, F. Wielonsky.
  
  Asymptotic uniqueness of best rational approximants of given degree to Markov functions in $L^2$ of the circle, in: Constr. Approx., 2001, vol. 17, n^o 1, pp. 103–138.
• 52L. Baratchart, M. Yattselev.
  
  Convergent interpolation to Cauchy integrals over analytic arcs, in: Found. Comp. Math., 2009, vol. 9, n^o 6, pp. 675–715.
• 53L. Baratchart, M. Yattselev.
  
  Meromorphic approximants for complex Cauchy transforms with polar singularities, in: Mat. Sbornik, 2009, vol. 200, n^o 9, pp. 3-40.
• 54L. Baratchart, M. Yattselev.
  
  Asymptotic uniqueness of best rational approximants to complex Cauchy transforms in $L^2$ of the circle, in: Recent trends in orthogonal polynomials and approximation theory, Providence, RI, Contemp. Math., Amer. Math. Soc., 2010, vol. 507, pp. 87–111.
• 55L. Baratchart, M. Yattselev.
  
  Convergent Interpolation to Cauchy Integrals over Analytic Arcs with Jacobi-Type Weights, in: International Mathematics Research Notices, 2010, vol. 2010, n^o 22, pp. 4211–4275.
  
  http://hal.inria.fr/hal-00508314
• 56A. Ben Abda, F. Ben Hassen, J. Leblond, M. Mahjoub.
  
  Sources recovery from boundary data: a model related to electroencephalography, in: Mathematical and Computer Modelling, 2009, vol. 49, n^o 11–12, pp. 2213–2223.
  
  http://dx.doi.org/10.1016/j.mcm.2008.07.016
• 57S. Bila, D. Baillargeat, M. Aubourg, S. Verdeyme, P. Guillon, F. Seyfert, J. Grimm, L. Baratchart, C. Zanchi, J. Sombrin.
  
  Direct Electromagnetic Optimization of Microwave Filters, in: IEEE Microwave Magazine, 2001, vol. 1, pp. 46–51.
• 58J. Blum.
  
  Numerical simulation and optimal control in plasma physics, with applications to Tokamaks, Wiley/Gauthier-Villars, 1989.
• 59R. Cameron, A. Harish, C. Radcliffe.
  
  Synthesis of advanced microwave filters without diagonal cross-couplings, in: IEEE Transactions on Microwave Theory and Techniques, dec 2002, vol. 50, n^o 12, pp. 2862–2872.
  
  http://dx.doi.org/10.1109/TMTT.2002.805141
• 60S. Chaabane, I. Fellah, M. Jaoua, J. Leblond.
  
  Logarithmic stability estimates for a Robin coefficient in 2D Laplace inverse problems, in: Inverse Problems, 2004, vol. 20, n^o 1, pp. 49–57.
  
  http://dx.doi.org/10.1088/0266-5611/20/1/003
• 61S. Chaabi.
  
  Analyse complexe et problèmes de Dirichlet dans le plan : équation de Weinstein et autres conductivités non bornées, Mathématiques et Informatique de Marseille, 2013.
• 62R. Coifman, R. Rochberg, G. Weiss.
  
  Factorization theorems for Hardy spaces in several variables, in: Ann. Math., 1976, vol. 103, pp. 611–635.
• 63Y. Fischer.
  
  Approximation des des classes de fonctions analytiques généralisées et résolution de problèmes inverses pour les tokamaks, Univ. Nice Sophia Antipolis, 2011.
  
  http://tel.archives-ouvertes.fr/tel-00643239/
• 64A. Friedman, M. Vogelius.
  
  Determining cracks by boundary measurements, in: Indiana Univ. Math. J., 1989, vol. 38, n^o 3, pp. 527–556.
• 65P. Fulcheri, M. Olivi.
  
  Matrix rational $H^2$-approximation: a gradient algorithm based on Schur analysis, in: SIAM J. on Control & Optim., 1998, vol. 36, pp. 2103–2127.
• 66J. B. Garnett.
  
  Bounded analytic functions, Academic Press, 1981.
• 67T. Georgiou.
  
  A topological approach to Nevanlinna-Pick interpolation, in: SIAM J. Math. Anal., 1987, vol. 18, n^o 5, pp. 1248–1260.
• 68J. Helton, D. Marshall.
  
  Frequency domain analysis and analytic selections, in: Indiana Univ. Math. J., 1990, vol. 39, n^o 1, pp. 157–184.
• 69T. Iwaniec, G. Martin.
  
  Geometric function theory and non-linear analysis, Oxford Univ. Press, 2001.
• 70B. Jacob, J. Leblond, J.-P. Marmorat, J. R. Partington.
  
  A constrained approximation problem arising in parameter identification, in: Linear Algebra and its Applications, 2002, vol. 351-352, pp. 487-500.
• 71N. Landkhof.
  
  Foundations of modern potential theory, Springer-Verlag, 1972.
• 72M. Lavrentiev.
  
  Some Improperly Posed Problems of Mathematical Physics, Springer, 1967.
• 73S. Lefteriu, M. Oldoni, M. Olivi, F. Seyfert.
  
  De-embedding multiplexers by Schur reduction, in: CDC - Conférence on Decision and Control, Florence, Italy, December 2013.
  
  http://hal.inria.fr/hal-00904794
• 74H. Orchard, G. Temes.
  
  Filter Design Using Transformed Variables, in: IEEE Transactions on Circuit Theory, dec 1968, vol. 15, n^o 4, pp. 385–408.
  
  http://dx.doi.org/10.1109/TCT.1968.1082870
• 75V. Peller.
  
  Hankel Operators and their Applications, Springer, 2003.
• 76A. Schneck.
  
  Constrained Hardy space approximation, in: J. Approx. Theory, 2010, vol. 8, pp. 1466–1483.
• 77I. Schur.
  
  Über Potenzreihen die im innern des einheitskreises beschränkt sind, in: J. Reine Angew. Math., 1917, vol. 147, pp. 205–232.
• 78F. Seyfert, L. Baratchart, J.-P. Marmorat, S. Bila, J. Sombrin.
  
  Extraction of coupling parameters for microwave filters: determinati on of a stable rational model from scattering data, in: 2003 IEEE MTT-S International Microwave Symposium Digest, Philadelphie, États-Unis, IEEE, 2003, vol. 1, pp. 25–28.
  
  http://hal.inria.fr/hal-00663504
• 79F. Seyfert, M. Oldoni, G. Macchiarella, D. Pacaud.
  
  De-embedding response of filters from diplexer measurements, in: International Journal of RF and Microwave Computer-Aided Engineering, August 2012, vol. 23, n^o 2, pp. 188–199.
  
  http://hal.inria.fr/hal-00763665
• 80E. M. Stein.
  
  Harmonic Analysis, Princeton University Press, 1993.
• 81P. K. Suetin.
  
  Polynomials orthogonal over a region and Bieberbach polynomials, Proc. Steklov Inst. Math., 1971, vol. 100, A.M.S. Transl. 1974.
• 82A. Suàrez, R. Quéré.
  
  Stability analysis of nonlinear microwave circuits, Artech House, 2003.
• 83T. Wolff.
  
  Counterexamples with harmonic gradients in ${𝐑}^3$, in: Essays on Fourier analysis in honor of Elias M. Stein, Math. Ser., Princeton Univ. Press, 1995, vol. 42, pp. 321–384.