Branquinho, Amílcar; Foulquié-Moreno, Ana; Fradi, Assil; Mañas, Manuel Matrix Jacobi biorthogonal polynomials via Riemann-Hilbert problem. (English) Zbl 07757742 Proc. Am. Math. Soc. 152, No. 1, 193-208 (2024). MSC: 33C45 42C05 39A36 39A12 34M50 15A16 PDFBibTeX XMLCite \textit{A. Branquinho} et al., Proc. Am. Math. Soc. 152, No. 1, 193--208 (2024; Zbl 07757742) Full Text: DOI arXiv
Fernández-Irisarri, Itsaso; Mañas, Manuel Laguerre-Freud equations for three families of hypergeometric discrete orthogonal polynomials. (English) Zbl 07771112 Stud. Appl. Math. 151, No. 2, 509-535 (2023). Reviewer: Faitori Omer Salem (Tripoli) MSC: 33E30 33C20 11B37 42C05 39A70 PDFBibTeX XMLCite \textit{I. Fernández-Irisarri} and \textit{M. Mañas}, Stud. Appl. Math. 151, No. 2, 509--535 (2023; Zbl 07771112) Full Text: DOI arXiv OA License
Gharakhloo, Roozbeh; Witte, Nicholas S. Modulated bi-orthogonal polynomials on the unit circle: the \(2j-k\) and \(j-2k\) systems. (English) Zbl 1525.33007 Constr. Approx. 58, No. 1, 1-74 (2023). Reviewer: Marcel G. de Bruin (Heemstede) MSC: 33C45 11C08 11M50 39A06 42C05 47B35 PDFBibTeX XMLCite \textit{R. Gharakhloo} and \textit{N. S. Witte}, Constr. Approx. 58, No. 1, 1--74 (2023; Zbl 1525.33007) Full Text: DOI arXiv
Chen, Xiao-Min; Chang, Xiang-Ke; He, Yi; Hu, Xing-Biao Generalized discrete Lotka-Volterra equation, orthogonal polynomials and generalized epsilon algorithm. (English) Zbl 1510.37113 Numer. Algorithms 92, No. 1, 335-375 (2023). MSC: 37K60 37K20 39A14 39A36 33C45 15A15 PDFBibTeX XMLCite \textit{X.-M. Chen} et al., Numer. Algorithms 92, No. 1, 335--375 (2023; Zbl 1510.37113) Full Text: DOI
Forrester, Peter J.; Kumar, Santosh Differential recurrences for the distribution of the trace of the \(\beta\)-Jacobi ensemble. (English) Zbl 1496.81091 Physica D 434, Article ID 133220, 11 p. (2022). MSC: 81U35 15B52 33C45 65Q30 47B10 39B42 PDFBibTeX XMLCite \textit{P. J. Forrester} and \textit{S. Kumar}, Physica D 434, Article ID 133220, 11 p. (2022; Zbl 1496.81091) Full Text: DOI arXiv
Sakhnovich, Alexander Discrete self-adjoint Dirac systems: asymptotic relations, Weyl functions and Toeplitz matrices. (English) Zbl 1486.39024 Constr. Approx. 55, No. 2, 641-659 (2022). MSC: 39A45 15B05 30E10 34B20 39A12 33C45 PDFBibTeX XMLCite \textit{A. Sakhnovich}, Constr. Approx. 55, No. 2, 641--659 (2022; Zbl 1486.39024) Full Text: DOI arXiv
Chang, Xiang-Ke; Li, Shi-Hao; Tsujimoto, Satoshi; Yu, Guo-Fu Two-parameter generalizations of Cauchy bi-orthogonal polynomials and integrable lattices. (English) Zbl 1466.37054 J. Nonlinear Sci. 31, No. 2, Paper No. 30, 23 p. (2021). MSC: 37K20 37K60 37K10 15A15 39A36 33C45 PDFBibTeX XMLCite \textit{X.-K. Chang} et al., J. Nonlinear Sci. 31, No. 2, Paper No. 30, 23 p. (2021; Zbl 1466.37054) Full Text: DOI arXiv
Branquinho, Amílcar; Huertas, Edmundo J. The symmetrization problem for multiple orthogonal polynomials. (English) Zbl 1460.33005 Marcellán, Francisco (ed.) et al., Orthogonal polynomials: current trends and applications. Proceedings of the 7th EIBPOA conference, Universidad Carlos III de Madrid, Leganés, Spain, July 3–6, 2018. Cham: Springer. SEMA SIMAI Springer Ser. 22, 17-51 (2021). MSC: 33C45 39B42 PDFBibTeX XMLCite \textit{A. Branquinho} and \textit{E. J. Huertas}, SEMA SIMAI Springer Ser. 22, 17--51 (2021; Zbl 1460.33005) Full Text: DOI arXiv
Abdalla, M. Fractional operators for the Wright hypergeometric matrix functions. (English) Zbl 1482.33002 Adv. Difference Equ. 2020, Paper No. 246, 14 p. (2020). MSC: 33C05 33C45 33C20 26A33 39A70 PDFBibTeX XMLCite \textit{M. Abdalla}, Adv. Difference Equ. 2020, Paper No. 246, 14 p. (2020; Zbl 1482.33002) Full Text: DOI
da Fonseca, Carlos M. On the connection between tridiagonal matrices, Chebyshev polynomials, and Fibonacci numbers. (English) Zbl 1498.15035 Acta Univ. Sapientiae, Math. 12, No. 2, 280-286 (2020). MSC: 15B05 11B39 15A15 15B36 33C45 39A10 PDFBibTeX XMLCite \textit{C. M. da Fonseca}, Acta Univ. Sapientiae, Math. 12, No. 2, 280--286 (2020; Zbl 1498.15035) Full Text: DOI
Choque-Rivero, Abdon E. The matrix Toda equations for coefficients of a matrix three-term recurrence relation. (English) Zbl 1432.37090 Oper. Matrices 13, No. 4, 1125-1145 (2019). MSC: 37K10 33C45 37J35 15A24 39A36 PDFBibTeX XMLCite \textit{A. E. Choque-Rivero}, Oper. Matrices 13, No. 4, 1125--1145 (2019; Zbl 1432.37090) Full Text: DOI
Chan, Chuan-Tsung; Liu, Hsiao-Fan A \(q\)-generalization of the Toda equations for the \(q\)-Laguerre/Hermite orthogonal polynomials. (English) Zbl 1416.33026 Random Matrices Theory Appl. 7, No. 4, Article ID 1840002, 20 p. (2018). MSC: 33D45 39A45 PDFBibTeX XMLCite \textit{C.-T. Chan} and \textit{H.-F. Liu}, Random Matrices Theory Appl. 7, No. 4, Article ID 1840002, 20 p. (2018; Zbl 1416.33026) Full Text: DOI arXiv
Yafaev, D. R. Analytic scattering theory for Jacobi operators and Bernstein-Szegö asymptotics of orthogonal polynomials. (English) Zbl 1397.81067 Ge, Mo-Lin (ed.) et al., Ludwig Faddeev memorial volume. A life in mathematical physics. Hackensack, NJ: World Scientific (ISBN 978-981-3233-76-8/hbk; 978-981-3233-87-4/ebook). 567-613 (2018). MSC: 81Q05 39A12 81U20 81Q10 33C45 39A70 47A40 47B39 PDFBibTeX XMLCite \textit{D. R. Yafaev}, in: Ludwig Faddeev memorial volume. A life in mathematical physics. Hackensack, NJ: World Scientific. 567--613 (2018; Zbl 1397.81067) Full Text: DOI arXiv
Odake, Satoru; Sasaki, Ryu Orthogonal polynomials from Hermitian matrices. II. (English) Zbl 1387.81213 J. Math. Phys. 59, No. 1, 013504, 42 p. (2018). Reviewer: Giovanni Rastelli (Vercelli) MSC: 81Q05 42C05 15B57 33C45 33E30 39A10 47B36 PDFBibTeX XMLCite \textit{S. Odake} and \textit{R. Sasaki}, J. Math. Phys. 59, No. 1, 013504, 42 p. (2018; Zbl 1387.81213) Full Text: DOI arXiv
Calogero, Francesco Finite-dimensional representations of difference operators and the identification of remarkable matrices. (English) Zbl 1312.39024 J. Math. Phys. 56, No. 3, 033506, 23 p. (2015). MSC: 39A70 33C45 33D45 PDFBibTeX XMLCite \textit{F. Calogero}, J. Math. Phys. 56, No. 3, 033506, 23 p. (2015; Zbl 1312.39024) Full Text: DOI arXiv
Kalateh Bojdi, Z.; Ahmadi-Asl, S.; Aminataei, A. The generalized Laguerre matrix method or solving linear differential-difference equations with variable coefficients. (English) Zbl 1301.33014 Appl. Appl. Math. 9, No. 1, 272-294 (2014). MSC: 33C45 39A10 34K06 PDFBibTeX XMLCite \textit{Z. Kalateh Bojdi} et al., Appl. Appl. Math. 9, No. 1, 272--294 (2014; Zbl 1301.33014) Full Text: Link
Branquinho, Amílcar; Moreno, Ana Foulquié; Mendes, Ana Matrix Orthogonal Polynomial in the theory of Full Kostant-Toda Systems. arXiv:1305.2644 Preprint, arXiv:1305.2644 [math.CA] (2013). MSC: 33C45 39B42 47N20 34K99 42C05 BibTeX Cite \textit{A. Branquinho} et al., ``Matrix Orthogonal Polynomial in the theory of Full Kostant-Toda Systems'', Preprint, arXiv:1305.2644 [math.CA] (2013) Full Text: arXiv OA License
Ismail, Mourad E. H.; Koelink, Erik Spectral analysis of certain Schrödinger operators. (English) Zbl 1270.30003 SIGMA, Symmetry Integrability Geom. Methods Appl. 8, Paper 061, 19 p. (2012). MSC: 30E05 33C45 39A10 42C05 44A60 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{E. Koelink}, SIGMA, Symmetry Integrability Geom. Methods Appl. 8, Paper 061, 19 p. (2012; Zbl 1270.30003) Full Text: DOI arXiv
Branquinho, A.; Rebocho, M. N. Difference and differential equations for deformed Laguerre-Hahn orthogonal polynomials on the unit circle. (English) Zbl 1269.33011 J. Phys. A, Math. Theor. 44, No. 46, Article ID 465204, 12 p. (2011). Reviewer: Tatiana Hessami Pilehrood (Mogilev) MSC: 33C45 39B42 PDFBibTeX XMLCite \textit{A. Branquinho} and \textit{M. N. Rebocho}, J. Phys. A, Math. Theor. 44, No. 46, Article ID 465204, 12 p. (2011; Zbl 1269.33011) Full Text: DOI
Branquinho, A.; Marcellán, F.; Mendes, A. Vector interpretation of the matrix orthogonality on the real line. (English) Zbl 1219.33007 Acta Appl. Math. 112, No. 3, 357-383 (2010). Reviewer: Chrysoula G. Kokologiannaki (Patras) MSC: 33C45 39B42 PDFBibTeX XMLCite \textit{A. Branquinho} et al., Acta Appl. Math. 112, No. 3, 357--383 (2010; Zbl 1219.33007) Full Text: DOI arXiv
Branquinho, A.; Rebocho, M. N. Matrix Sylvester equations in the theory of orthogonal polynomials on the unit circle. (English) Zbl 1196.33006 Bull. Belg. Math. Soc. - Simon Stevin 17, No. 2, 355-376 (2010). Reviewer: Alicia Cachafeiro López (Vigo) MSC: 33C45 33C47 39B42 42C05 PDFBibTeX XMLCite \textit{A. Branquinho} and \textit{M. N. Rebocho}, Bull. Belg. Math. Soc. - Simon Stevin 17, No. 2, 355--376 (2010; Zbl 1196.33006) Full Text: Euclid
Felipe, Raúl Discrete orthogonal matrix polynomials. (English) Zbl 1205.42025 Anal. Math. 35, No. 3, 189-197 (2009). MSC: 42C05 33C45 33D45 39A12 PDFBibTeX XMLCite \textit{R. Felipe}, Anal. Math. 35, No. 3, 189--197 (2009; Zbl 1205.42025) Full Text: DOI
Odake, Satoru; Sasaki, Ryu Orthogonal polynomials from Hermitian matrices. (English) Zbl 1152.81575 J. Math. Phys. 49, No. 5, 053503, 43 p. (2008). MSC: 42C05 15B57 33C45 33E30 39A10 47B36 81Q05 PDFBibTeX XMLCite \textit{S. Odake} and \textit{R. Sasaki}, J. Math. Phys. 49, No. 5, 053503, 43 p. (2008; Zbl 1152.81575) Full Text: DOI arXiv
Aceto, L.; Trigiante, D. Pascal matrix, classical polynomials and difference equations. (English) Zbl 1127.39001 Elaydi, S. (ed.) et al., Difference equations, special functions and orthogonal polynomials. Proceedings of the international conference, Munich, Germany, July 25–30, 2005. Hackensack, NJ: World Scientific (ISBN 978-981-270-643-0/hbk). 1-16 (2007). MSC: 39A05 15B57 33C45 15B36 PDFBibTeX XMLCite \textit{L. Aceto} and \textit{D. Trigiante}, in: Difference equations, special functions and orthogonal polynomials. Proceedings of the international conference, Munich, Germany, July 25--30, 2005. Hackensack, NJ: World Scientific. 1--16 (2007; Zbl 1127.39001)
Pedersen, Steen Absolutely continuous Jacobi operators. (English) Zbl 1028.33009 Proc. Am. Math. Soc. 130, No. 8, 2369-2376 (2002). Reviewer: J.Saurer (Regensburg) MSC: 33C45 39A70 47A10 47B39 PDFBibTeX XMLCite \textit{S. Pedersen}, Proc. Am. Math. Soc. 130, No. 8, 2369--2376 (2002; Zbl 1028.33009) Full Text: DOI
Van Assche, Walter Nonsymmetric linear difference equations for multiple orthogonal polynomials. (English) Zbl 0962.42016 Levi, Decio (ed.) et al., SIDE III - Symmetries and integrability of difference equations. Proceedings of the 3rd conference, Sabaudia, Italy, May 16-22, 1998. Providence, RI: American Mathematical Society (AMS). CRM Proc. Lect. Notes. 25, 415-429 (2000). MSC: 42C05 39A10 33C45 37K60 47B36 PDFBibTeX XMLCite \textit{W. Van Assche}, in: SIDE III -- Symmetries and integrability of difference equations. Proceedings of the 3rd conference, Sabaudia, Italy, May 16--22, 1998. Providence, RI: American Mathematical Society (AMS). 415--429 (2000; Zbl 0962.42016)
Duran, Antonio J. Ratio asymptotics for orthogonal matrix polynomials. (English) Zbl 0944.42015 J. Approximation Theory 100, No. 2, 304-344 (1999). Reviewer: A.Martínez Finkelshtein (Almeria) MSC: 42C05 33C45 30E15 47A56 39A11 PDFBibTeX XMLCite \textit{A. J. Duran}, J. Approx. Theory 100, No. 2, 304--344 (1999; Zbl 0944.42015) Full Text: DOI
Jódar, L.; Company, R. Hermite matrix polynomials and second order matrix differential equations. (English) Zbl 0858.15014 Approximation Theory Appl. 12, No. 2, 20-30 (1996). Reviewer: G.P.A.Thijsse (Rotterdam) MSC: 15A54 34A30 33C50 33C45 39A10 PDFBibTeX XMLCite \textit{L. Jódar} and \textit{R. Company}, Approximation Theory Appl. 12, No. 2, 20--30 (1996; Zbl 0858.15014)
Sun, Jiachang An identity for a tridiagonal determinant and its applications. (Chinese. English summary) Zbl 0537.15003 Math. Numer. Sin. 4, 323-327 (1982). MSC: 15A15 15A18 33C45 39A10 PDFBibTeX XMLCite \textit{J. Sun}, Math. Numer. Sin. 4, 323--327 (1982; Zbl 0537.15003)