Dr. Ricardo Abreu Blaya

Productividad Académica

Artículos

• Axial Inframonogenic Functions In Clifford Analysis: DA Santiesteban et al. DA Santiesteban, RA Blaya, B Schneider. Complex Analysis and Operator Theory 19 (7), 193.
• A jump problem for an iterated Lamé–Navier system in Rm. MA Herrera Pelaez, R Abreu Blaya, A Moreno García, JM Sigarreta Almira .Boletín de la Sociedad Matemática Mexicana 31 (2), 1-27.
• Generalizaciones de la Ecuación de Laplace desde el Análisis de Clifford. JLS Ricardo, DA Santiesteban, RA Blaya. Revista Politécnica 55 (2), 43-54.
• A Cauchy–Kowalevski theorem for ψ-bimonogenic functions. JLS Ricardo, RA Blaya. Georgian Mathematical Journal. https://doi.org/10.1515/gmj-2025-2035.
• On the Dirichlet problem for bianalytic functions. A Moreno García, J Radilla Villaseñor, R Abreu Blaya. Complex Variables and Elliptic Equations, 1-12.
• On Second Order Elliptic Systems of Partial Differential Equations in Clifford Analysis. D Alfonso Santiesteban, R Abreu Blaya, J Bory Reyes. Advances in Applied Clifford.
• Descomposiciones aditivas del vector de desplazamiento del sistema de Lamé-Navier. D Alfonso-Santiesteban, R Abreu-Blaya, JL Sánchez-Santiesteban. Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales.
• On irregularity integral Sombor indices: theory and chemical applications. R Abreu-Blaya, J Batanero, JM Rodríguez, JM Sigarreta. Journal of Mathematical Chemistry 63 (3), 731-748.
• On the well-posedness of boundary value problems for higher order Dirac operators in Rm. DA Santiesteban, RA Blaya, JB Reyes. Journal of Differential Equations 416, 1729-1746.
• A jump problem for an iterated Lamé–Navier system in Rm. MAH Pelaez, RA Blaya, AM García, JMS Almira. Boletín de la Sociedad Matemática Mexicana: Tercera Serie 31 (2), 9.
• Quaternionic and Clifford Analysis for Non-smooth Domains. RA Blaya, JB Reyes. Operator Theory, 1-32.
• On the Well-Posedness of Boundary Value Problems for Higher Order Dirac Operators in RM. DA Santiesteban, RA Blaya, JB Reyes. Journal of Differential Equations 416, 1729-1746.
• Fractional Fischer decompositions by inframonogenic functions. DA Santiesteban, RA Blaya, YP Pérez, JMS Almira. Journal of Mathematical Analysis and Applications 539 (1), 128468.
• Reconstruction of multivectorial fields in Clifford analysis. R Abreu-Blaya, J Bory-Reyes, T Moreno-García, D Alfonso-Santiesteban. Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales.
• Reconstrucción de campos multivectoriales apartir del análisis de Clifford. R Abreu-Blaya, J Bory-Reyes, T Moreno-García, D Alfonso-Santiesteban. Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales.
• Hardy decomposition of first order Lipschitz functions by Clifford algebra-valued harmonic functions. L De la Cruz Toranzo, RA Blaya, S Bernstein. Journal of Mathematical Analysis and Applications 536 (1), 128242.
• Reduction procedure for obtaining solutions of the scalar additive Jump problem and Riemann boundary value problem in vectorial Clifford analysis. CD Tamayo Castro, J Bory Reyes, R Abreu Blaya. Mathematical Methods in the Applied Sciences 47 (11), 8611-8625.
• Lipschitz Norm Estimate for a Higher Order Singular Integral Operator. TR Gómez Santiesteban, R Abreu Blaya, JC Hernández Gómez. Advances in Applied Clifford Algebras 34 (3), 14.
• Hardy decomposition of higher order Lipschitz classes by polymonogenic functions. LDC Toranzo, RA Blaya, S Bernstein. arXiv preprint arXiv:2404.16447.
• Generalizaciones del operador de Lamé-Navier en análisis de Clifford. DA Santiesteban, DEG Valencia, RA Blaya, YP Pérez. Publicaciones e Investigación 18 (1).
• Two Spheres Uniquely Determine Infrabimonogenic Functions. LMM Alvarez, AM García, MPÁ Alejandre, RA Blaya. Mediterranean Journal of Mathematics 20 (6), 318.
• On a Riemann–Hilbert problem for -hyperholomorphic functions in. JLS Ricardo, RA Blaya, JS Ortiz. Analysis and Mathematical Physics 13 (6), 84.
• On the generalized Fourier transform. R Abreu‐Blaya, JM Rodríguez, JM Sigarreta. Mathematical Methods in the Applied Sciences 46 (16), 16709-16733.
• Boundary value problems for a second‐order elliptic partial differential equation system in Euclidean space. D Alfonso Santiesteban, R Abreu Blaya, J Bory Reyes. Mathematical Methods in the Applied Sciences 46 (14), 15784-15798.
• Dirichlet problem for electromagnetic fields in chiral media with fractal boundary. LMA Nápoles, RÁ Ávila, RA Blaya, YP Pérez. Chaos, Solitons & Fractals 174, 113879.
• On a generalized Klausmeier model. MPC de la Cruz, DA Santiesteban, LMM Álvarez, RA Blaya, HGJ Carlos. Mathematical Biosciences and Engineering 20 (9), 16447-16470.
• On the Dirichlet problem for second order elliptic systems in the ball. AM García, DA Santiesteban, RA Blaya. Journal of Differential Equations 364, 498-520.
• Decomposition of first order Lipschitz functions by Clifford algebra-valued harmonic functions. LDC Toranzo, RA Blaya, S Bernstein. arXiv preprint arXiv:2305.15838.
• Decomposition of first order Lipschitz functions by Clifford algebra-valued harmonic functions. L De la Cruz Toranzo, RA Blaya, S Bernstein. arXiv preprint arXiv:2305.15838.
• Sets of uniqueness for infrapolymonogenic functions. AM García, LMM Álvarez, RA Blaya. Mediterranean Journal of Mathematics 20 (1), 28.
• On the Riemann problem in fractal elastic media. DEG Valencia, RA Blaya, MPÁ Alejandre, YP Pérez. Analysis and Mathematical Physics 13 (1), 3.
• Buscando estructuras en las soluciones de un sistema generalizado de Lame-Navier. DA Santiesteban, RA Blaya, MPÁ Alejandre. Publicaciones e Investigación 17 (1).
• El problema de Riemann para el sistema de Lamé-Navier bidimensional. DEG Valencia, DA Santiesteban, RA Blaya. Ciencias Matemáticas 36 (1), 43-49.
• Moreno García, Arsenio; Moreno García, Tania; Abreu Blaya, Ricardo. Comparing harmonic and inframonogenic functions in Clifford analysis. Mediterr. J. Math. 19 (2022), no. 1, Paper No. 33, 14 pp.
• Santiesteban, Tania Rosa Gómez; Abreu Blaya, Ricardo; Hernández Gómez, Juan C.; Sigarreta Almira, José María. A Cauchy transform for polymonogenic functions on fractal domains. Complex Anal. Oper. Theory 16 (2022), no. 3, Paper No. 42, 16 pp.
• Ricardo, José Luis Serrano; Abreu Blaya, Ricardo; Bory Reyes, Juan; Sánchez Ortiz, Jorge. On a Riemann-Hilbert boundary value problem for $(\varphi, \psi)$-harmonic functions in $\Bbb R^m$. Georgian Math. J. 29 (2022), no. 3, 445--454.
• Abreu Blaya, Ricardo; Alfonso Santiesteban, Daniel; Bory Reyes, Juan; Moreno García, Arsenio. Inframonogenic decomposition of higher-order Lipschitz functions. Math. Methods Appl. Sci. 45 (2022), no. 9, 4911--4928.
• Alfonso Santiesteban, Daniel; Abreu Blaya, Ricardo. Isomorphisms of partial differential equations in Clifford analysis. Adv. Appl. Clifford Algebr. 32 (2022), no. 1, Paper No. 10, 18 pp.
• Cruz, Martha Paola; Abreu-Blaya, Ricardo; Bosch, Paul; Rodríguez, José M.; Sigarreta, José M. On Ostrowski type inequalities for generalized integral operators. J. Math. 2022, Art. ID 2247246, 9 pp.
• Herrera Peláez, Marcos Antonio; Abreu Blaya, Ricardo; García, Arsenio Moreno; Sigarreta Almira, José María. Integral representation formulas for higher order Dirac equations. J. Math. Anal. Appl. 515 (2022), no. 2, Paper No. 126414, 17 pp. 
• Avila Alfaro, Marisel; Abreu Blaya, Ricardo. Complex and quaternionic Cauchy formulas in Koch snowflakes. Complex Var. Elliptic Equ. 67 (2022), no. 6, 1287--1298. 
• JL Serrano Ricardo, J Bory Reyes, R Abreu Blaya (2021). Singular integral operators and a ∂-problem for (phi, Psi)-harmonic functions. Analysis and Mathematical Physics 11 (4).                    
• R Abreu Blaya, MPC De la Cruz, JL Sánchez Santiesteban, J. M. Sigarreta Almira. (2021). Riemann problem for bianalytic functions on h-summable curves. Complex Variables and Elliptic Equations, 1-14, 2021.
• DA Santiesteban, RA Blaya, MPÁ Alejandre (2021). On (ϕ,ψ) -Inframonogenic Functions in Clifford Analysis. Bulletin of the Brazilian Mathematical Society, New Series, 1-17, 2021.              
• J Bory-Reyes, R Abreu-Blaya, MA Pérez-de la Rosa, B Schneider (2021). Hilbert and Poincaré-Bertrand Formulas in Polyanalytic Function Theory Involving Higher Order Lipschitz Classes. Complex Analysis and Operator Theory 15 (5), 1-13, 2021.           
• CD Tamayo-Castro, R Abreu-Blaya, J Bory-Reyes (2021). On Riemann problems for monogenic functions in lower dimensional non-commutative Clifford algebras. Analysis and Mathematical Physics 11 (2), 1-19, 2021.
• DEG Valencia, RA Blaya, MPÁ Alejandre, AM García (2021). On the Plane Lamé–Navier System in Fractal Domains. Complex Analysis and Operator Theory 15 (3), 1-15, 2021.
• R Abreu-Blaya, R Reyes, JM Rodríguez, JM Sigarreta (2021). Inequalities on the generalized atom bond connectivity index. Journal of Mathematical Chemistry 59 (3), 775-791, 2021.
• RA Blaya. (2021). A Riemann jump problem for biharmonic functions in fractal domains. Analysis and Mathematical Physics 11 (1), 1-13, 2021.                    
• R Abreu-Blaya, S Bermudo, JM Rodríguez, E Tourís (2021). Topological Indices and f-Polynomials on Some Graph Products. Symmetry 13 (2), 292.
• RA Blaya, L De la Cruz Toranzo (2021). Polyanalytic Hardy decomposition of higher order Lipschitz functions. Journal of Mathematical Analysis and Applications 493 (2), 124559.
• RA Blaya, JA Mendez-Bermudez, AM García, JM Sigarreta (2021). Boundary value problems for the Lamé-Navier system in fractal domains. AIMS Mathematics 6 (10), 221, 10449-10465.
• J Bory-Reyes, R Abreu-Blaya, MA Pérez-de la Rosa, B Schneider (2020). Integral formulas of the Hilbert, Poincaré-Bertrand, Schwarz and Poisson type for the β–analytic function theory. Journal of Mathematical Analysis and Applications 492 (2), 124493. 2020.                        
• R Abreu-Blaya, J Bory-Reyes, MA Herrera-Peláez, JM Sigarreta-Almira (2020). Integral Representation Formulas Related to the Lamé—Navier System. Acta Mathematica Sinica, English Series 36 (12), 1341-1356. 2020.
• Abreu-Blaya, R., Bory-Reyes, J., Moreno-García, A., and Moreno-García, T. (2020). A Cauchy Integral Formula for Infrapolymonogenic Functions in Clifford Analysis. Advances in Applied Clifford Algebras, 30, 1-17. 10.1007/s00006-020-1049-x. 
• Abreu-Blaya, R., Fleitas, A., Nápoles-Valdés, J. E., Reyes, R., Rodríguez, J. M., and Sigarreta, J. M. (2020). On the conformable fractional logistic models. Mathematical Methods in the Applied Sciences, 43(7), 4156-4167. 10.1002/mma.6180.
• Peña-Pérez, Y., Abreu-Blaya, R., Árciga-Alejandre, M. P., and Bory-Reyes, J. (2020). Biquaternionic reformulation of a fractional monochromatic Maxwell system. Advances in High Energy Physics, 1-9. 10.1155/2020/6894580.
• Peña-Pérez, Y., Abreu-Blaya, R., Bosch, P., and Bory-Reyes, J. (2020). Dirichlet type problem for 2D quaternionic time-harmonic Maxwell system in fractal domains. Advances in Mathematical Physics, 1-8. 10.1155/2020/4735357. 
• Moreno-Garcia, A., Moreno-Garcia, T.,  Abreu-Blaya, R., and Bory-Reyes, J. (2020). Decomposition of inframonogenic functions with applications in elasticity theory. Mathematical Methods in the Applied Sciences, 43(4), 1915-1924. 10.1002/mma.6015. 
• Bory-Reyes, J.,  Abreu-Blaya, R., Pérez-de la Rosa, M. A., and Schneider, B. (2019). Correction to: Poincaré-Bertrand and Hilbert formulas for the Cauchy-Cimmino singular integrals [MR3718173].  Advances in Applied Clifford Algebras, 29(2), Paper No. 31, 2 pp.
• Bory-Reyes, J., Abreu-Blaya, R., Rodríguez-Dagnino, R. M., and Kats, B. A. (2019). On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation.Analysis and Mathematical Physics, 9(1), 483–496. 
• Abreu-Blaya, R., Bory-Reyes, J., Morales-Amaya, E., and Sigarreta-Almira, J. M. (2019) On the self-conjugateness of differential forms on bounded domains. Revista de la Unión Matemática Argentina, 60(1), 247–256.
• De la Cruz-Toranzo, L., Abreu-Blaya, R., and Bory-Reyes, J. (2019). On the Plemelj–Privalov theorem in Clifford analysis involving higher order Lipschitz classes.  Journal of Mathematical Analysis and Applications. 480(2),  1-13. 10.1016/j.jmaa.2019.123411.
• De la Cruz-Toranzo, L., Moreno-García, A., Moreno-García, T., Abreu-Blaya, R., and Bory-Reyes, J. (2019). A bimonogenic Cauchy transform on higher order Lipschitz classes. Mediterranean Journal of Mathematics, 16(1), Paper No. 13, 1-14. 
• Tamayo-Castro, C. D., Abreu-Blaya, R., and Bory-Reyes, J. (2019). Compactness of embedding of generalized higher order Lipschitz classes. Analysis and Mathematical Physics, 9(4), 1719–1727. 
• Moreno-García, A., Moreno-García, T., Abreu-Blaya, R., and Bory-Reyes, J. (2018). Inframonogenic functions and their applications in 3-dimensional elasticity theory. Mathematical Methods in the Applied Sciences, 41(10), 3622–3631. 
• Bory-Reyes, J., Abreu-Blaya, R., Pérez-de la Rosa, M. A., and Schneider, B. (2018). On the Hilbert formulas on the unit circle for α-hyperholomorphic function theory. Complex Variables and Elliptic Equations, 63(11), 1509–1528.
• Bory-Reyes, J., Abreu-Blaya, R., Árciga-Alejandre, M. P., and Peña-Pérez, Y. (2018). Riemann and Dirichlet type problems for hyperanalytic functions in fractal domains. Complex Analysis and Operator Theory, 12(5), 1369–1382.
• Bory-Reyes, J., Abreu-Blaya, R., Pérez-de la Rosa, M. A., and Schneider, B. (2018). On the Hilbert formulas and of change of integration order for some singular integrals in the unit circle. Turkish Journal of Mathematics, 42(3), 862–875. 
• Gómez-Santiesteban, T. R., Abreu-Blaya, R., Bory-Reyes, J., and Sigarreta-Almira, J. M. (2018). A Cauchy transform for polyanalytic functions on fractal domains. Annales Polonici Mathematici, 121(1), 21–32.
• De la Cruz-Toranzo, L., Abreu-Blaya, R., and Bory-Reyes, J. (2018). The Plemelj-Privalov theorem in polyanalytic function theory. Journal of Mathematical Analysis and Applications, 463(2), 517–533.
• Bory-Reyes, J., Abreu-Blaya, R., Pérez-de la Rosa, M. A., and Schneider, B. (2017). A quaternionic treatment of inhomogeneous Cauchy-Riemann type systems in some traditional theories. Complex Analysis and Operator Theory, 11(5), 1017–1034.
• Bory-Reyes, J., De la Cruz-Toranzo, L., and Abreu-Blaya, R. (2017). Singular integral operator involving higher order Lipschitz classes. Mediterranean Journal of Mathematics, 14(2), Paper No. 38, 1-13.
• Peña-Pérez, Y., Árciga-Alejandre, M. P., Abreu-Blaya, R., and Bory-Reyes, J. (2017).  Hölder norm estimate for the fractal Hilbert transform in Douglis analysis. Journal of Inequalities and Applications, Paper No. 213, 1-11.
• Bory-Reyes, J., Abreu-Blaya, R., Pérez-de la Rosa, M. A., and Schneider, B. (2017). Poincaré-Bertrand and Hilbert formulas for the Cauchy-Cimmino singular integrals. Advances in Applied Clifford Algebras, 27(4), 2933–2960.
• Moreno-García, A., Moreno-García, T., Abreu-Blaya, R., and Bory-Reyes, J. (2017). A Cauchy integral formula for inframonogenic functions in Clifford analysis. Advances in Applied Clifford Algebras, 27(2), 1147–1159.
• Abreu-Blaya, R., Bory-Reyes, J., Guzmán-Adán, A., and Kähler, U. (2017). On the φ-hyperderivative of the ψ-Cauchy-type integral in Clifford analysis. Computational Methods and Function Theory, 17(1), 101–119. 
• Bory-Reyes, J., Abreu-Blaya, R., Pérez-de la Rosa, M. A., and Schneider, B. (2017). On the 2D quaternionic metaharmonic layer potentials. Mediterranean Journal of Mathematics, 14(5), Paper No. 195, 1-18.
• Abreu-Blaya, R., De la Cruz-Toranzo, L., Gómez-Santiesteban, T. R., Ramírez-Leyva, Y., and Bory-Reyes, J. (2017). Cauchy integral operators involving higher order Lipschitz classes in the poly-analytic function theory. Bulletin of the Brazilian Mathematical Society, 48(2), 253–260.
• Bory-Reyes, J., Tamayo-Castro, C. D., and Abreu-Blaya, R. (2017). Compound Riemann Hilbert boundary value problems in complex and quaternionic analysis. Advances in Applied Clifford Algebras, 27(2), 977–991.
• Segura-Vidal, C., Parra-Inza, E., Tamayo-Cuenca, R., and Abreu-Blaya, R. (2017). GeAWeb: Virtual Learning Object for Analytic Geometry. Journal for Educators, Teachers and Trainers, 8, 91-112. 
• Bory-Reyes, J., Abreu-Blaya, R., Hernández-Simon, L. M., and Schneider, B. (2016). Dirichlet-type problems for the two-dimensional Helmholtz operator in complex quaternionic analysis. Mediterranean Journal of Mathematics, 13(6), 4901–4916.
• Abreu-Blaya, R., Bory-Reyes, J., Guzmán-Adán, A., and Kähler, U. (2016). On the Π-operator in Clifford analysis. Journal of Mathematical Analysis and Applications, 434(2), 1138–1159.
• Abreu-Blaya, R., Bory-Reyes, J., Guzmán-Adán, A., and Kähler, U. (2015). On some structural sets and a quaternionic (φ,ψ)-hyperholomorphic function theory. Mathematische Nachrichten, 288(13), 1451–1475.
• Abreu-Blaya, R., Ávila-Ávila, R., Bory-Reyes, J., and Rodríguez-Dagnino, R. M. (2015). Cauchy representation formulas for Maxwell equations in 3-dimensional domains with fractal boundaries. Bulletin of the Brazilian Mathematical Society, 46(4), 681–700.
• Abreu-Blaya, R., Ávila-Ávila, R., and Bory-Reyes, J. (2015). Boundary value problems with higher order Lipschitz boundary data for polymonogenic functions in fractal domains. Applied Mathematics and Computation, 269, 802–808.
• Abreu-Blaya, R., Ávila-Ávila, R., Bory-Reyes, J., and Rodríguez-Dagnino, R. M. (2015). 2D quaternionic time-harmonic Maxwell system in elliptic coordinates. Advances in Applied Clifford Algebras, 25(2), 255–270.
• Abreu-Blaya, R., Bory-Reyes, J., Brackx, F., De Schepper, H., Moreno-García, T., and Sommen, F. (2015). Boundary value problems on fractal hypersurfaces for the quaternionic Hermitian system in R4n. Complex Analysis and Operator Theory, 9(5), 957–973.
• Abreu-Blaya, R., Ávila-Ávila, R., and Bory-Reyes, J. (2015). Boundary value problems for Dirac operators and Maxwell's equations in fractal domains. Mathematical Methods in the Applied Sciences, 38(3), 393–402.
• Abreu-Blaya, R., Bory-Reyes, J., and Kats, B. (2015). Cauchy integral and singular integral operator over closed Jordan curves. Monatshefte für Mathematik, 176(1), 1–15.
• Abreu-Blaya, R., Bory-Reyes, J., and Rodríguez-Dagnino, R. M. (2015). Boundary value problems for hyperholomorphic solutions of two dimensional Helmholtz equation in a fractal domain. Applied Mathematics and Computation, 261, 183–191.
• Abreu-Blaya, R., and Bory-Reyes, J. (2015). Jump conditions for a metaharmonic double layer potential on rectifiable closed Jordan curves in R2. Annales Polonici Mathematici, 115(2), 179–188.

Capítulos de Libros

• Abreu-Blaya, R., and Bory-Reyes, J. (2015). Quaternionic and Clifford Analysis for Non-smooth Domains. En Alpay, D (Ed.). Operator Theory, 1447-1470. 10.1007/978-3-0348-0667-1_31.