1). J. C. García-Ardila, F. Marcellán, M. E. Marriaga,
Orthogonal Polynomials and Linear Functionals. An Algebraic Approach and Applications. EMS Series of Lectures in Mathematics, EMS Press, Berlin, 2021 ISBN: 978-3-98547-008-2
21). D. Dominici, J. C. García-Ardila, F. Marcellán,
Symmetrization process and truncated orthogonal polynomials, Anal. Math. Phys. 14, 137 (2024).
20). G. Ariznabarreta, J. C. García-Ardila, M. Mañas, F. Marcellán,
Uvarov perturbations for matrix orthogonal polynomials, Proc. Amer. Math. Soc. Ser. B 11 (2024), 525-537.
19). J. C. García-Ardila, F. Marcellán,
Generalized Gauss-Rys orthogonal polynomials, J. Math. Anal. Appl. 540, 2, 128695, 23 pp. (2024).
18). J. C. García-Ardila, F. Marcellán,
Spectral transformations and second kind polynomials associated with a hermitian linear functional. Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 118, 79 (2024).
17). J. C. García-Ardila, M. E. Marriaga,
Approximation by polynomials in Sobolev spaces associated with classical moment functionals. Numer. Algor 95, 285–318 (2024).
16). J. C. García-Ardila,
15). J. C. García-Ardila, M. E. Marriaga,
Sobolev orthogonality of polynomial solutions of second order partial differential equations. Comput. Appl. Math. 42, 13, (2023)
14). J. C. García-Ardila, F. Marcellán, P. H. Villamil-Hernández,
Associated orthogonal polynomials of the first kind and Darboux transformations. J. Math. Anal. Appl. 508, 2, 125883, 26 pp. (2022).
13). J. C. García-Ardila, M. E. Marriaga,
On Sobolev bilinear forms and polynomial solutions of second-order differential equations. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 115, 191 (2021)
12). J. C. García-Ardila, F. Marcellán,
Spectral Transformations and Associated Linear Functionals of the First Kind. Axioms, 10, 107 (2021)
11). A. Branquinho, J. C. García-Ardila, F. Marcellán,
Ratio Asymptotics for biorthogonal matrix polynomials with unbounded recurrence coefficients. Appl. Anal. Discret. Math. 14 (2020), 754–774
10). D. Barrios-Rolanía, J. C. García-Ardila, D. Manrique,
On the Darboux transformations and sequences of p-orthogonal polynomials. Appl. Math. Comput, 382, (2020), 125337.
JCR® 2020 Impact Factor: 4.091 - Q1 (7/265) - T1
9). A. Branquinho, Ana Foulquié-Moreno J. C. García-Ardila,
Matrix Toda and Volterra lattices. Appl. Math. Comput. 365 (2020), 124722
8). D. Barrios-Rolanía J. C. García-Ardila,
Geronimus transformations for sequences of d-orthogonal polynomials. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 114: 26, (2020)
7). J. C. García-Ardila, M. Mañas, F. Marcellán,
Christoffel Transformation for a Matrix of Bi-variate Measures. Complex Anal. Oper. Theory. 13 no. 8 3979-4005. (2019)
6). G. Ariznabarreta, J. C. García-Ardila, M. Mañas, F. Marcellán,
Matrix biorthogonal polynomials on the real line Geronimus transformations. Bull. Math. Sci. 9 no. 2 (2019). 1950007 (68 pages).
5). G. Ariznabarreta, J. C. García-Ardila, M. Mañas, F. Marcellán,
Non-Abelian integrable hierarchies: matrix biorthogonal polynomials and perturbations. J. Phys. A: Math. Theor. (2018) 51, 205204
4). J. C. García-Ardila, L. E. Garza, F. Marcellán,
A canonical Geronimus transformation for matrix orthogonal polynomials. Linear Multilinear Algebra. 66 (2018), 357-381
3). C. Álvarez-Fernández, G. Ariznabarreta, J. C. García-Ardila, M. Mañas, F. Marcellán,
Christoffel transformations for matrix orthogonal polynomials in the real line and the non-Abelian 2D Toda lattice hierarchy. Internat. Math. Res. Notices, (2017) 2017 issue 5, 1285–1341
2). J. C. García-Ardila, L. E. Garza, F. Marcellán,
An Extension of the Geronimus Transformation for Orthogonal Matrix Polynomials on the Real Line. Mediterr. J. Math. (2016) 13, 5009-5032
1). M. Derevyagin, J. C. García-Ardila, F. Marcellán,
Multiple Geronimus transformations. Linear Algebra Appl. 454 (2014), 158-183.
4). J. C. García-Ardila, F. Marcellán,
A note on Laguerre truncated polynomials and quadrature formula. M. Stanić, M. Albijanić, D. Djurčić, M. Spalević (eds) Analysis, Approximation, Optimization: Computation and Applications. Springer Optimization and Its Applications, 224. Springer, Cham. (2025)
3). D. Barrios-Rolanía, J. C. García-Ardila,
A note on banded linear systems. Journal of Pure and Applied Mathematics: Advances and Applications 26, 1, 1-23. (2023).
2). J. C. García-Ardila, F. Marcellán, M.E. Marriaga,
From Standard Orthogonal Polynomials to Sobolev Orthogonal Polynomials: The Role of Semiclassical Linear Functionals. Foupouagnigni M., Koepf W. (eds) Orthogonal Polynomials. AIMSVSW 2018. Tutorials, Schools, and Workshops in the Mathematical Sciences. Birkhäuser, Cham (2020)
1). H. Dueñas, J. C. García-Ardila, L. Garza, A. Ramírez,
The Diagonal General Case of the Laguerre-Sobolev Type Orthogonal Polynomials. Revista Colombiana de Matemáticas 47 (1) (2013), 39-66.