List of Publications
Bidiagonal factorization of recurrence banded matrices in mixed multiple orthogonality (Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié Moreno, Hélder Lima and Manuel Mañas) https://arxiv.org/abs/2410.15363
Classical discrete multiple orthogonal polynomials: hypergeometric and integral representations (Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié Moreno, Manuel Mañas and Thomas Wolfs) https://arxiv.org/abs/2409.16254
Integral and hypergeometric representations for multiple orthogonal polynomials (Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié Moreno Manuel Mañas and Thomas Wolfs) https://arxiv.org/abs/2407.15001
Semiclassical orthogonal polynomials on the unit circle: A Riemann-Hilbert perspective (Amílcar Branquinho, Ana Foulquié Moreno and Karina Rampazzi) https://doi.org/10.48550/arXiv.2406.07290
Banded totally positive matrices and normality for mixed multiple orthogonal polynomials (Amílcar Branquinho, Ana Foulquié Moreno and Manuel Mañas) https://doi.org/10.48550/arXiv.2404.13965
Classical multiple orthogonal polynomials for arbitrary number of weights and their explicit representation (Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié Moreno and Manuel Mañas) https://doi.org/10.48550/arXiv.2404.13958
Hypergeometric multiple orthogonal polynomials and Random Walk (Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié Moreno and Manuel Mañas) https://doi.org/10.48550/arXiv.2107.00770
2021—
Finite Markov chains and multiple orthogonal polynomials (Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié Moreno and Manuel Mañas) Journal of Computational and Applied Mathematics (2024) accepted, https://doi.org/10.48550/arXiv.2308.00182
Matrix orthogonal polynomials: A Riemann-Hilbert approach (Amílcar Branquinho, Assil Fradi, Ana Foulquié Moreno and Manuel Mañas), Coimbra Mathematical Texts, Vol. 3, Chapter 2 (2024) DOI: 10.1007/978-3-031-69646-6_2, https://doi.org/10.48550/arXiv.2305.19954
Hypergeometric expressions for type I Jacobi-Piñeiro orthogonal polynomials with arbitrary number of weights (Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié Moreno and Manuel Mañas) Proceedings of the American Mathematical Society, Ser. B, 11 (2024) 200-210, DOI: https://doi.org/10.1090/bproc/225, https://doi.org/10.48550/arXiv.2310.18294
Lax-type pairs in the theory of bivariate orthogonal polynomials (Amílcar Branquinho, Ana Foulquié Moreno, Teresa E. Pérez and Miguel Piñar) Linear Algebra and Its Applications (2024) DOI: https://doi.org/10.1016/j.laa.2024.03.020, https://doi.org/10.48550/arXiv.2311.05949
Bidiagonal factorization of the recurrence matrix for the Hahn multiple orthogonal polynomials (Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié Moreno and Manuel Mañas) Linear Algebra and Its Applications (2024) DOI: https://doi.org/10.1016/j.laa.2024.03.033, https://doi.org/10.48550/arXiv.2308.01288
Markov chains and multiple orthogonality (Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié Moreno and Manuel Mañas) To appear in ''Orthogonal Polynomials, Special Functions and Applications - Proceedings of the 16th International Symposium, Montreal, Canada, In honor to Richard Askey'', the CRM Series in Mathematical Physiscs, 2023, accepted, https://doi.org/10.48550/arXiv.2304.04414
Banded matrices and their orthogonality (Amílcar Branquinho, Ana Foulquié Moreno and Manuel Mañas) In Recent Progress in Special Functions, Galina Filipuk, editor, AMS Contemporary Mathematics, Vol. 807, Chapter 1 (2024) https://doi.org/10.48550/arXiv.2307.08081
Matrix Jacobi biorthogonal polynomials via Riemann-Hilbert problem (Amílcar Branquinho, Ana Foulquié Moreno, Assil Fradi and Manuel Mañas) Proceedings of the American Mathematical Society, 152(1) (2024) 193-208, DOI: https://doi.org/10.1090/proc/16431, https://arxiv.org/abs/2209.15372
Jacobi-Piñeiro Markov chains (Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié Moreno, Manuel Mañas, and Carlos Álvarez-Fernández) Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 118 (15) (2024) DOI: https://doi.org/10.1007/s13398-023-01510-x, https://doi.org/10.48550/arXiv.2103.13715
Spectral theory for bounded banded matrices with positive bidiagonal factorization and mixed multiple orthogonal polynomials (Amílcar Branquinho, Ana Foulquié Moreno and Manuel Mañas) Advances in Mathematics 434 (2023) 109313, DOI: https://doi.org/10.1016/j.aim.2023.109313, https://doi.org/10.48550/arXiv.2212.10235
Positive bidiagonal factorization of tetradiagonal Hessenberg matrices (Amílcar Branquinho, Ana Foulquié Moreno and Manuel Mañas) Linear Algebra and its Applications, 677 (2023) 132-160, DOI: https://doi.org/10.1016/j.laa.2023.08.001, https://arxiv.org/abs/2210.10728
Oscillatory banded Hessenberg matrices, multiple orthogonal polynomials and Markov chains (Amílcar Branquinho, Ana Foulquié Moreno and Manuel Mañas) Physica Scipta 98 (2023) 105223, DOI: 10.1088/1402-4896/ace93d, https://arxiv.org/abs/2203.13578
Hahn multiple orthogonal polynomials of type I: Hypergeometrical expressions (Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié Moreno and Manuel Mañas) Journal of Mathematical Analysis and Applications, 528 (2023) 127471, DOI: https://doi.org/10.1016/j.jmaa.2023.127471, https://doi.org/10.48550/arXiv.2212.11923
Bidiagonal factorization of tetradiagonal matrices and Darboux transformations (Amílcar Branquinho, Ana Foulquié Moreno and Manuel Manas) Analysis and Mathematical Physics, 13, 42 (2023), DOI: 10.1007/s13324-023-00801-1, https://arxiv.org/abs/2210.10727
Monomial and Rodrigues orthogonal polynomials on the cone (Rabia Aktas, Amílcar Branquinho, Ana Foulquié Moreno and Yuan Xu) Journal of Mathematical Analysis and Applications 522 (2023) 126977, DOI: https://doi.org/10.1016/j.jmaa.2022.126977, https://arxiv.org/abs/2208.12954
Quadratic decomposition of bivariate orthogonal polynomials (Amílcar Branquinho, Ana Foulquié Moreno and Teresa E. Pérez) Mediterranean Journal of Mathematical 20, 118 (2023), DOI: 10.1007/s00009-023-02307-3, https://doi.org/10.48550/arxiv.2202.09575
Multiple orthogonal polynomials: Pearson equations and Christoffel formulas (Amílcar Branquinho, Ana Foulquié Moreno and Manuel Mañas) Analysis and Mathematical Physics 12(6), 129 (2022), DOI: https://doi.org/10.1007/s13324-022-00734-1
Riemann-Hilbert problem for the matrix Laguerre biorthogonal polynomials: The matrix discrete Painlevé IV (Amílcar Branquinho, Ana Foulquié Moreno, Assil Fradi and Manuel Mañas) Mathematics, 10(8) (2022), 1205, DOI: https://www.mdpi.com/2227-7390/10/8/1205, Pré-publicações do DMUC 19-26
Matrix biorthogonal polynomials: eigenvalue problems and non-abelian discrete Painlevé equations (Amílcar Branquinho, Ana Foulquié Moreno and Manuel Mañas) J. Math. Anal. Appl. 494 (2) (2021) 124605, DOI: 10.1016/j.jmaa.2020.124605, Pré-publicações do DMUC 18-26
Riemann-Hilbert problem and matrix biorthogonal polynomials (Amílcar Branquinho, Ana Foulquié Moreno and Manuel Mañas) In: Orthogonal Polynomials: Current Trends and Applications, F. Marcellán and E.J. Huertas (eds.), SEMA SIMAI Springer Series vol. 22 (2021) 1-15, DOI: 10.1007/978-3-030-56190-1_1, Pré-publicações do DMUC 19-10
The symmetrization problem for multiple orthogonal polynomials (Amílcar Branquinho and Edmundo J. Huertas Cejudo) In: Orthogonal Polynomials: Current Trends and Applications, F. Marcellán and E.J. Huertas (eds.), SEMA SIMAI Springer Series 22 (2021) 17-51, DOI: 10.1007/978-3-030-56190-1_2
2016—2020
Matrix Toda and Volterra lattices (Amílcar Branquinho, Ana Foulquié Moreno and J.C. García-Ardila) Applied Mathematics and Computation, 365 (2020) 124722, DOI: 10.1016/j.amc.2019.124722, Pré-publicações do DMUC 19-16
Ratio asymptotic for biorthogonal matrix polynomials with unbounded recurrence coefficients (Amílcar Branquinho, J.C. García-Ardila and F. Marcellán) Appl. Anal. Discrete Math. 14 (3) (2020) 754-774, DOI: 10.2298/AADM190225051B, Pré-publicações do DMUC 17-27
A characterization theorem for semi-classical orthogonal polynomials on non uniform lattices (Amílcar Branquinho, Y. Chen, G. Filipuk and M.N. Rebocho) Applied Mathematics and Computation, 334 (2018) n. 1, 356-366, DOI: 10.1016/j.amc.2018.04.022, Pré-publicações do DMUC 18-08
Orthogonal polynomial interpretation of q-Toda and q-Volterra equations (Ivan Area, Amílcar Branquinho, Ana Foulquié Moreno and Eduardo Godoy) Bulletin of the Malaysian Mathematical Sciences Society, 41 (2018) n. 1, 393–414, DOI: 10.1007/s40840-016-0305-7, Pré-publicações do DMUC 16-02
Characterizations of classical orthogonal polynomials on quadratic lattices (M. Njinkeu Sandjon, Amílcar Branquinho, M. Foupouagnigni and Ivan Area) Journal of Difference Equations and Applications, 23 (2017) n. 6, 983-1002, DOI: 10.1080/10236198.2017.1307972, arXiv:1604.00186
Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials (Amílcar Branquinho, Ana Foulquié Moreno and A. Mendes) Integral Transforms and Special Functions, 28 (2017) n. 1, 74-90, DOI: 10.1080/10652469.2016.1250082
Matrix biorthogonal polynomials, associated polynomials and functions of the second kind (Amílcar Branquinho, J.C. García-Ardila and F. Marcellán) Pré-publicações do DMUC 17-39
Characterizations of Δ-Volterra lattice: A symmetric orthogonal polynomials interpretation (Ivan Area, Amílcar Branquinho, Ana Foulquié Moreno and Eduardo Godoy) Journal of Mathematical Analysis and Applications, 433 (2016) n.1, 243-259, DOI: dx.doi.org/10.1016/j.jmaa.2015.07.051, Pré-publicações do DMUC 15-50
2011—2015
Orthogonal polynomial interpretation of Δ-Toda equations (Ivan Area, Amílcar Branquinho Ana Foulquié Moreno and Eduardo Godoy) Journal of Physics A: Mathematical and Theoretical, 48 (2015) 405206, DOI: http://dx.doi.org/10.1088/1751-8113/48/40/405206, Pré-publicações do DMUC 14-25
Second order differential equations in the Laguerre-Hahn class (Amílcar Branquinho, Ana Foulquié Moreno, Anabela Paiva and M.N. Rebocho) Applied Numerical Mathematics, 94 (2015) 16–32, DOI: http://dx.doi.org/10.1016/j.apnum.2015.03.002, Pré-publicações do DMUC 12-13
Characterization theorem for Laguerre-Hahn orthogonal polynomials on non-uniform lattices (Amílcar Branquinho and M.N. Rebocho) Journal of Mathematical Analysis and Applications 427 (2015) n. 1, pp. 185-201, DOI: 10.1016/j.jmaa.2015.02.044, Pré-publicações do DMUC 13-21
Zeros of orthogonal polynomials generated by the Geronimus perturbation of measures (Amílcar Branquinho, Edmundo J. Huertas Cejudo and Fernando R. Rafaeli) Lecture Notes in Computer Science, 8579, B. Murgante et al. (Eds.): ICCSA 2014, 44–59, ISBN 978-3-319-09152-5, DOI: 10.1007/978-3-319-09144-0_4, pré-publicações do DMUC 14-07
Deformed Laguerre-Hahn orthogonal polynomials on the real line (Amílcar Branquinho and M.N. Rebocho) Applied Mathematics and Computation, 233 (2014) 359–368, DOI: 10.1016/j.amc.2014.02.019, Pré-publicações do DMUC 13-02
Sylvester equations for Laguerre-Hahn orthogonal polynomials on the real line (Amílcar Branquinho, Anabela Paiva and M.N. Rebocho) Applied Mathematics and Computation, 219 (2013) 9118-9131, DOI: 10.1016/j.amc.2013.03.083, Pré-publicações do DMUC 12-24
On the full Kostant Toda system and the discrete Korteweg-de Vries equations (D. Barrios Rolanía, Amílcar Branquinho and Ana Foulquié Moreno) Journal of Mathematical Analysis and Applications, 401 (2013) n. 2, 811-820, DOI: 10.1016/j.jmaa.2012.12.050, Pré-publicações do DMUC 12-15
Relative asymptotics for orthogonal matrix polynomials (Amílcar Branquinho, F. Marcellán and A. Mendes) Linear Algebra and Its Applications, 437 (2012) n. 7, 1458-1481, DOI: 10.1016/j.laa.2012.04.032, Pré-publicações do DMUC 10-09
Structure relations for orthogonal polynomials on the unit circle (Amílcar Branquinho and M.N. Rebocho) Linear Algebra and Its Applications 436 (2012) n.11, 4296-4310, DOI: 10.1016/j.laa.2012.01.034, Pré-publicações do DMUC 11-27
On the semi-classical character of orthogonal polynomials satisfying structure relations (Amílcar Branquinho and M.N. Rebocho) Journal of Difference Equations and Applications 18 (2012) n. 1, 111-138, DOI: 10.1080/10236198.2010.529137, Pré-publicações do DMUC 10-06
Difference and differential equations for deformed Laguerre-Hahn orthogonal polynomials on the unit circle (Amílcar Branquinho and M.N. Rebocho) Journal of Physics A: Mathematical and Theoretical, 44 (2011) n. 46, 465204, DOI: 10.1088/1751-8113/44/46/465204, Pré-publicações do DMUC 11-10
On the relation between the full Kostant-Toda lattice and multiple orthogonal polynomials (D. Barrios Rolanía, Amílcar Branquinho and Ana Foulquié Moreno) Journal of Mathematical Analysis and Applications, 377 (2011) n. 1, 228-238, DOI: 10.1016/j.jmaa.2010.10.044,Pré-publicações do DMUC 09-43
2006—2010
Vector interpretation of the matrix orthogonality on the real line (Amílcar Branquinho, F. Marcellán and A. Mendes) Acta Applicandae Mathematicae, 112 (2010) n. 3, 357-383, DOI: 10.1007/s10440-010-9577-3, Pré-publicações do DMUC 09-41
Algebraic theory of multiple orthogonal polynomials (Amílcar Branquinho, L. Cotrim and Ana Foulquié Moreno) Pré-publicações do DMUC 09-08
Matrix interpretation of multiple orthogonality (Amílcar Branquinho, L. Cotrim and Ana Foulquié Moreno) Numerical Algorithms, 55 (2010) n. 1, 19-37, DOI: 10.1007/s11075-009-9355-3, Pré-publicações do DMUC 08-57
Matrix Sylvester equations in the theory of orthogonal polynomials on the unit circle (Amílcar Branquinho and M.N. Rebocho) Bulletin of the Belgian Mathematical Society -- Simon Stevin, 17 (2010) n. 2, 355-376, DOI: 10.36045/bbms/1274896211, Pré-publicações do DMUC 08-16
Dynamics and interpretation of some integrable systems via multiple orthogonal polynomials (D. Barrios Rolanía, Amílcar Branquinho and Ana Foulquié Moreno) Journal of Mathematical Analysis and Applications, 361(2010) n. 2, 358-370, DOI: 10.1016/j.jmaa.2009.07.025, Pré-publicações do DMUC 08-54
Riemann-Hilbert problem associated with Angelesco systems (Amílcar Branquinho, U. Fidalgo Prieto and Ana Foulquié Moreno) Journal of Computational and Applied Mathematics, 233 (2009) n. 3, 643-651, DOI: 10.1016/j.cam.2009.02.032
Distributional equation for Laguerre-Hahn functionals on the unit circle (Amílcar Branquinho and M.N. Rebocho) Journal of Computational and Applied Mathematics, 233 (2009) n. 3, 634-642, DOI: 10.1016/j.cam.2009.02.031, Pré-publicações do DMUC 07-34
On differential equations for orthogonal polynomials on the unit circle (Amílcar Branquinho and M.N. Rebocho) Journal of Mathematical Analysis and Applications, 356 (2009) n. 1, 242-256, DOI: 10.1016/j.jmaa.2009.03.008, Pré-publicações do DMUC 08-33
Complex high order Toda and Volterra lattices (D. Barrios Rolanía and Amílcar Branquinho) Journal of Difference Equations and Applications, 15 (2009) n. 2, 197-213, DOI: 10.1080/10236190802019491, Pré-publicações do DMUC 08-07
Coherent pairs of linear functionals on the unit circle (Amílcar Branquinho, Ana Foulquié Moreno, F. Marcellán and M.N. Rebocho) Journal of Approximation Theory, 153 (2008) n. 1, 122-137, DOI: 10.1016/j.jat.2008.03.003, Pré-publicações do DMUC 07-27
Characterizations of Laguerre-Hahn affine orthogonal polynomials on the unit circle (Amílcar Branquinho and M.N. Rebocho) Journal of Computational Analysis and Applications, 10 (2008) n. 2, 229-242, Pré-publicações do DMUC 07-03
Coimbra Lecture Notes on Orthogonal Polynomials (Amílcar Branquinho and Ana Foulquié Moreno) Advances in the Theory of Special Functions and Orthogonal Polynomials, Nova Science Publishers, Inc., New York, 2008, ISBN: 1-60021-972-1
1997—2005
Normal indices in Nikishin systems (Amílcar Branquinho, J. Bustamante, Ana Foulquié Moreno and G. López) Journal of Approximation Theory, 124 (2003) n. 2, 254-262, DOI: 10.1016/j.jat.2003.09.009
Padé approximants and complex high order Toda lattices (A.I. Aptekarev and Amílcar Branquinho) Journal of Computation and Applied Mathematics, 155 (2003) n. 2, 231-237, DOI: 10.1016/S0377-0427(02)00866-X
Multiple orthogonal polynomials for classical weights (A.I. Aptekarev, Amílcar Branquinho and W. Van Assche) Trans. Amer. Math. Soc., 355 (2003) n. 10, 3887-3914, DOI: 10.1090/S0002-9947-03-03330-0
Asymptotic behavior of Sobolev type orthogonal polynomials on a rectifiable Jordan Curve or Arc (Amílcar Branquinho, Ana Foulquié Moreno and F. Marcellán) Constructive Approximation, 18 (2002) n. 2, 161-182, DOI: 10.1007/s00365-001-0005-9
Six Years of Intensive Courses (Amílcar Branquinho, P. Cerejeiras, H. Malonek and J. Silva) Cadernos de Matemática CM00/I-08, DMUA
Orthogonal polynomials and rational modifications of Lebesgue measures on the unit circle. An inverse problem (Amílcar Branquinho, L. Golinskii and F. Marcellán) Complex Variables, 38 (1999) n. 2, 137-154, DOI: 10.1080/17476939908815160
Toda-Type differential equations for the recurrence coefficients of orthogonal polynomials and Freud transformation (with A.I. Aptekarev, Amílcar Branquinho and F. Marcellán) J. Comput. Appl. Math., 78 (1997) n. 1, 139-160, DOI: 10.1016/S0377-0427(96)00138-0
On inverse problems for orthogonal polynomials satisfying a differential-difference equation (Amílcar Branquinho, Ana Foulquié Moreno and F. Marcellán) Facta Universitatis, Series: Mathematics and Informatics, 12 (1997), 87-108
1993—1996
Problemas Inversos na Teoria dos Polinómios Ortogonais (Amílcar Branquinho) Tese de Doutoramento, Universidade Coimbra, Departamento de Matemática, Coimbra, Portugal, Outubro de 1996
A note on semi-classical orthogonal polynomials (Amílcar Branquinho) Bull. Belg. Math. Soc., 3 (1996), 1-12, DOI: 10.36045/bbms/1105540755
Generating new classes of orthogonal polynomials (Amílcar Branquinho and F. Marcellán) Inter. J. of Math. and Math. Sci., 19, (1996) n.4, 643-656, DOI: 10.1155/S0161171296000919
Some inverse problems for second order structure relations (Amílcar Branquinho and F. Marcellán) Approximation and Optimization (J.Guddat, ed.), Peter Lang, European Science Publishers, Frankfurt, 1995, 129-146
Classical orthogonal polynomials: A functional approach (Amílcar Branquinho, F. Marcellán and J. Petronilho) Acta Appl. Math., 34 (1994) n.3, 283-303, DOI: 10.1007/BF00998681
On inverse problems for orthogonal polynomials I (Amílcar Branquinho, F. Marcellán and J. Petronilho) J. Comput. Appl. Math., 49 (1993), 153-160, DOI: 10.1016/0377-0427(93)90146-3
A generalization of a theorem of S. Bochner (M. Alfaro, Amílcar Branquinho, F. Marcellán and J. Petronilho) Publicaciones del Seminario Matemático García Galdeano II, 11 (1992) n. 1, 9
