Dra. Teresa E. Pérez

Membership

• Full Professor of the Department of Applied Mathematics of the University of Granada
• Secretary of the research Institute IMAG-UGR , of the University of Granada
• Member of the Research Group GOYA - Research Group on Orthogonality and Applications , code FQM-384, supported by Junta de Andalucía (Spain).
• Leading of the ORTHONET: Spanish Network on Orthogonal Polynomials and Approximation Theory
• Member of the Real Sociedad Matemática Española (RSME)
• Member of the Sociedad Española de Matemática Aplicada (SEMA)
• Member of the American Mathematical Society (AMS)
• Member of the Society for Industry and Applied Mathematics (SIAM)

Profiles

• Profile on American Mathematical Society (AMS)
• Profile on Research ID
• Profile on Orcid

Research Subjects

• Approximation Theory, Orthogonal Polynomials and Special Functions
• Numerical Analysis

Recent Research Projects

• Multivariate Approximation with Applications, PID2023.149117NB.I00. Research Project of the National Plan. Ministry of Science, Innovation and Universities of Spain (MICINN), and the European Regional Development Fund (ERDF). Coordinators Miguel A. Piñar (UGR) and Teresa E. Pérez (UGR). Duration: from 09/01/2024 to 08/31/2027.
• Unit of Excelence «María de Maeztu» IMAG, CEX2020-001105-M. Centers and Units of Excellence. Ministry of Science, Innovation and Universities of Spain. Coordinator Joaquín Pérez Muñoz (UGR). Duration: from 2022 to 2025.
• GOYA - Group on Orthogonality and Applications, FQM-384 Research Group supported by Junta de Andalucía (Spain). Coordinator: Lidia Fernández (UGR). Duration: from 07/03/2017.

Publications

2026-2030

1. A. Branquinho, A. M. Delgado, T. E. Pérez, Simplex and generalized Disk Polynomials: Explicit relations and Partial Differential Equations.
2. T. E. Pérez, M. A. Piñar, M. J. Recarte, Bivariate Bernstein-type operators on the simplex. Standard and negative parameters.
   

2021-2025

1. C. F. Bracciali, A. M. Delgado, L. Fernández, T. E. Pérez, R_II type three term relations for bivariate polynomials orthogonal with respect to varying weights. Results in Mathematics 80 (2025), 206.
   Article
   MR4961449
   arXiv
2. A. Branquinho, A. Foulquié, T. E. Pérez, M. A. Piñar, Lax-type pairs in the theory of bivariate orthogonal polynomials. Linear Algebra Appl. 721 (2025), pages 219-239.
   Open Access
   MR4913737
   arXiv
3. C. F. Bracciali, G. S. Costa, T. E. Pérez, Centrosymmetric and reverse matrices in bivariate orthogonal polynomials. Linear Algebra Appl. 692 (2024), 212-240.
   Open Access
   MR4732924
   arXiv
4. L. Fernández, F. Marcellán, T. E. Pérez, M. A. Piñar, Sobolev orthogonal polynomials and spectral methods in boundary value problems. Appl. Numer. Math. 200 (2024), 254-272.
   Open Access
   MR4731107
5. L. Fernández, F. Marcellán, T. E. Pérez, M. A. Piñar, Sobolev orthogonal polynomials for solving the Schrödinger equation with potentials V(x) = x^{2k}, k > 1. In: Castillo, K., Durán, A.J. (eds) Orthogonal Polynomials and Special Functions. Coimbra Mathematical Texts 3 . Springer, Cham. 2024.
   DOI
6. D. Lara-Velasco, T. E. Pérez, Bernstein-type operators preserving derivatives. Comput. Appl. Math. 43 (2024), no. 5, Paper No. 277, 30 pp.
   Open Access
   MR4757556
7. A. Branquinho, A. Foulquié, T. E. Pérez, Quadratic decomposition of bivariate orthogonal polynomials. Medit. J. Math. 20 (2023), no. 3, 118.
   Open Access
   MR4549895
8. M. E. Marriaga, T. E. Pérez, M. A. Piñar, M. J. Recarte, Approximation via gradients on the ball. The Zernike case. J. Comput. Appl. Math. 430 (2023), Paper No. 115258
   Open Access
   MR4577313
9. M. E. Marriaga, T. E. Pérez, M. J. Recarte, Simultaneous approximation via laplacians on the unit ball. Medit. J. Math. 20 (2023), Article Number 316.
   Open Access
   MR4655120
10. M. J. Recarte, M. E. Marriaga, T. E. Pérez, A class of Bernstein-type operators on the unit disk. Bull. Malays. Math. Sci. Soc. 46 (2023), no. 4, 127.
    Open Access
    MR4596003
11. R. Aktas, I. Area, T. E. Pérez, Three term relations for multivariate Uvarov orthogonal polynomials. Comput. Appl. Math. 41 (2022), Article number: 330.
    Open Access
    MR4491185
12. C. F. Bracciali, G. S. Costa, T. E. Pérez, Two variable Freud orthogonal polynomials and matrix Painlevé-type difference equations. J. Differ. Equ. Appl. 28 (2022) 1157-1177.
    arXiv
    MR4502152
13. C. F. Bracciali, T. E. Pérez, Mixed orthogonality on the unit ball. Comput. Appl. Math. 40 (2021), no. 8, Paper No. 274.
    MR4325900
14. F. Lizarte, T. E. Pérez, M. A. Piñar, The radial part of a class of Sobolev polynomials on the unit ball. Numer. Algorithms 87 (2021), no. 4, 1369-1389.
    MR4287895
15. M. Marriaga, T. E. Pérez, M. A. Piñar, Bivariate Koornwinder-Sobolev orthogonal polynomials. Mediterr. J. Math. 18 (2021), no. 6, 234.
    MR4320531

2016-2020

1. F. Marcellán, M. E. Marriaga, T. E. Pérez, M. A. Piñar, Geronimus transformations of bivariate linear functionals. J. Math. Anal. Appl. 484 (2020), 123736, 30 pp.
   MR4040130
2. F. Marcellán, M. E. Marriaga, T. E. Pérez, M. A. Piñar, Coherent pairs of bivariate orthogonal polynomilas J. Approx. Theory 245 (2019), 40-63.
   MR3945603
3. A. M. Delgado, L. Fernández, T. E. Pérez, Fourth order partial differential equations for Krall-type orthogonal polynomials on the triangle. Proc. Amer. Math. Soc. 146 (2018), 3961-3974.
   MR3825849
4. F. Marcellán, M. Marriaga, T. E. Pérez, M. A. Piñar, On bivariate classical orthogonal polynomials. Appl. Math. Comput. 325 (2018), 340-357.
   MR3759149
5. F. Marcellán, M. Marriaga, T. E. Pérez, M. A. Piñar, Matrix Pearson equations satisfied by Koornwinder weights in two variables. Acta Appl. Math. 153 (2018), 81-100.
   MR3745731
6. C. F. Bracciali, T. E. Pérez, Bivariate orthogonal polynomials, 2D Toda lattices and Lax-type pairs. Appl. Math. Comput. 309 (2017), 142-155.
   MR3646384
7. M. Marriaga, T. E. Pérez, M. A. Piñar, Three term relations for a class of bivariate polynomials. Medit. J. Math. 14 (2017), no. 2, Art. 54, 26 pp.
   MR3619416
8. C. F. Bracciali, J. H. McCabe, T. E. Pérez, A. Sri Ranga, A class of orthogonal functions given by a three term recurrence formula. Math. Comp. 85 (2016), 1837-1859.
   MR3471110
9. A. M. Delgado, L. Fernández, D. S. Lubinsky, T. E. Pérez, M. A. Piñar, Sobolev orthogonal polynomials on the unit ball via outward derivatives. J. Math. Anal. Appl. 440 (2016), 716-740.
   MR3484991
10. A. M. Delgado, L. Fernández, T. E. Pérez, M. A. Piñar, Multivariate orthogonal polynomials and modified moment functionals. SIGMA Symmetry Integrability Geom. Methods Appl. 12 (2016), paper no. 090, 25 pp.
    MR3545477

2011-2015

1. L. Fernández, F. Marcellán, T. E. Pérez, M. Piñar, Y. Xu, Sobolev orthogonal polynomials on product domains. J. Comput. Appl. Math. 284 (2015), 202-215
   MR3319504
2. M. Alfaro, A. Peña, T. E. Pérez, M. L. Rezola, On linearly related orthogonal polynomials in several variables. Numer. Algorithms 66 (2014), 537-553.
   MR3225001
3. C. F. Bracciali, T. E. Pérez, M. Piñar, Stieltjes functions and discrete classical orthogonal polynomials. Comput. Appl. Math. 32 (2013), 537-547.
   MR3120139
4. T. E. Pérez, M. Piñar, Y. Xu, Weighted Sobolev orthogonal polynomials on the unit ball. J. Approx. Theory 171 (2013), 84-104.
   MR3053718
5. A. M. Delgado, T. E. Pérez, M. Piñar, Sobolev-type orthogonal polynomials on the unit ball. J. Approx. Theory 170 (2013), 94-106.
   MR3044047
6. A. M. Delgado, L. Fernández, T. E. Pérez, M. Piñar, On the Uvarov modification of two variable orthogonal polynomials on the disk. Complex Anal. Oper. Theory 6 (3) (2012), 665-676.
   MR2944078
7. L. Fernández, T. E. Pérez, M. Piñar, On Koornwinder classical orthogonal polynomials in two variables. J. Comput. Appl. Math. 236 (2012), 3817-3826.
   MR2923514
8. M. V. de Mello, V. G. Paschoa, T. E. Pérez, M. A. Piñar, Multivariate Sobolev-type orthogonal polynomials. Jaen J. Approx. 3 (2011), 241-259.
   MR2954375
9. J. J. Moreno-Balcázar, T. E. Pérez, M. A. Piñar, A generating function for non-standard orthogonal polynomials involving differences: the Meixner case. Ramanujan J. 25 (1) (2011), 21-35.
   MR2787289
10. L. Fernández, T. E. Pérez, M. A. Piñar, Orthogonal polynomials in two variables as solutions of higher order partial differential equations. J. Approx. Theory 163 (2011), 84-97.
    MR2741221

2006-2010

1. E. X. L. Andrade, C. F. Bracciali, M. V. de Mello, T. E. Pérez, Zeros for Jacobi-Sobolev orthogonal polynomials following non-coherent pair of measures. Comput. Appl. Math. 29 (2010), 423-445.
   MR2740662
2. C. F. Bracciali, A. M. Delgado, L. Fernández, T. E. Pérez, M. A. Piñar, New steps on Sobolev orthogonality in two variables. J. Comput. Appl. Math. 235 (2010), 916-926.
   MR2727629
3. A. M. Delgado, L. Fernández, T. E. Pérez, M. A. Piñar, Y. Xu, Orthogonal polynomials in several variables for measures with mass points. Numer. Algorithms 55 (2010), 245-264.
   MR2720631
4. L. Fernández, F. Marcellán, T. E. Pérez, M. A. Piñar, Recent Trends on Two Variable Orthogonal Polynomials Differential Algebra, Complex Analysis and Orthogonal Polynomials, P. Acosta-Humánez and F. Marcellán, eds. Contemporary Mathematics, 509, 59-86, American Mathematical Society, Providence, RI, 2010.
   MR2647637
   
5. L. Fernández, T. E. Pérez, M. A. Piñar, Y. Xu, Krall-type ortogonal polynomials in several variables. J. Comput. Appl. Math. 233 (2010), 1519-1524.
   MR2559340
   
6. M. Álvarez de Morales, L. Fernández, T. E. Pérez, M. A. Piñar, Bivariate ortogonal polynomials in the Lyskova class. J. Comput. Appl. Math. 233 (2009), 597-601.
   MR2582991
   
7. M. Álvarez de Morales, L. Fernández, T. E. Pérez, M. A. Piñar, A matrix Rodrigues formula for classical orthogonal polynomials in two variables. J. Approx. Theory 157 (2009), 32-52.
   MR2500152
   
8. M. Álvarez de Morales, L. Fernández, T. E. Pérez, M. A. Piñar, A Stieltjes function in two variables. Approximation Theory XII: San Antonio 2007, 1-13, Nashboro Press, Brentwood, TN, 2008.
   MR2537115
   
9. M. Álvarez de Morales, L. Fernández, T. E. Pérez, M. A. Piñar, A semiclassical perspective on multivariate orthogonal polynomials. J. Comput. Appl. Math. 214 (2008), 447-456.
   MR2398345
   
10. M. Álvarez de Morales, L. Fernández, T. E. Pérez, M. A. Piñar, On differential properties for multivariate orthogonal polynomials. Numer. Algorithms 45 (2007), no. 1-4, 153-166.
    MR2355979
    
11. M. Álvarez de Morales,L. Fernández, T. E. Pérez, M. A. Piñar, Semiclassical orthogonal polynomials in two variables. J. Comput. Appl. Math. 207 (2007), 323-330.
    MR2345250
    
12. L. Fernández, T. E. Pérez, M. A. Piñar, Second--order partial differential equations for gradients of orthogonal polynomials in two variables. J. Comput. Appl. Math. 199 (2007), 113-121.
    MR2267536
    

2001-2005

1. L. Fernández, T. E. Pérez, M. A. Piñar, On multivariate classical orthogonal polynomials. Rend. Circ. Mat. Palermo (2) Suppl. No. 76 (2005), 315-329.
   MR2178443
   
2. L. Fernández, T. E. Pérez, M. A. Piñar, Classical orthogonal polynomials in two variables: a matrix approach. Numer. Algorithms 39 (2005), no. 1-3, 131-142.
   MR2137747
   
3. L. Fernández, T. E. Pérez, M. A. Piñar, Weak classical orthogonal polynomials in two variables. J. Comput. Appl. Math. 178 (2005), no. 1-2, 191-203.
   MR2127879
4. M. Álvarez de Morales, T. E. Pérez, M. A. Piñar, Orthogonal polynomials associated with a Delta-Sobolev inner product. J. Difference Equ. Appl. 8 (2002), no. 2, 125-151.
   MR1882484
5. M. Alfaro, J. J. Moreno-Balcázar, T. E. Pérez, M. A. Piñar, M. L. Rezola, Asymptotics of Sobolev orthogonal polynomials for Hermite coherent pairs. J. Comput. Appl. Math. 133 (2001), no. 1-2, 141-150.
   MR1858274

1996-2000

1. M. Álvarez de Morales, J. J. Moreno-Balcázar, T. E. Pérez, M. A. Piñar, Nondiagonal Hermite-Sobolev orthogonal polynomials. Acta Appl. Math. 61 (2000), no. 1-3, 257-266.
   MR1783293
2. E. García-Caballero, T. E. Pérez, M. A. Piñar, Hermite interpolation and Sobolev orthogonality. Acta Appl. Math. 61 (2000), no. 1-3, 87-99.
   MR1783285
3. M. Alfaro, M. L. Rezola, T. E. Pérez, M. A. Piñar, On symmetric differential operators associated with Sobolev orthogonal polynomials: a characterization. Acta Appl. Math. 61 (2000), no. 1-3, 3-14.
   MR1783278
4. H. G. Meijer, T. E. Pérez, M. A. Piñar, Asymptotics of Sobolev orthogonal polynomials for coherent pairs of Laguerre type. J. Math. Anal. Appl. 245 (2000), no. 2, 528-546.
   MR1758554
5. M. Alfaro, T. E. Pérez, M. A. Piñar, M. L. Rezola, Sobolev orthogonal polynomials: the discrete-continuous case. Methods Appl. Anal. 6 (1999), no. 4, 593-616.
   MR1795525
6. E. García-Caballero, T. E. Pérez, M. A. Piñar, Sobolev orthogonal polynomials: interpolation and approximation. Electron. Trans. Numer. Anal. 9 (1999), 56-64 (electronic).
   MR1749798
7. M. Álvarez de Morales, T. E. Pérez, M. A. Piñar, A. Ronveaux, Non-standard orthogonality for Meixner polynomials. Electron. Trans. Numer. Anal. 9 (1999), 1-25 (electronic).
   MR1749794
8. M. Álvarez de Morales, T. E. Pérez, M. A. Piñar, Sobolev orthogonality for the Gegenbauer polynomials {C^(-N+1/2)}_{n>0}. J. Comput. Appl. Math. 100 (1998), no. 1, 111-120.
   MR1658734
9. T. E. Pérez, M. A. Piñar, Sobolev orthogonality and properties of the generalized Laguerre polynomials. Orthogonal functions, moment theory, and continued fractions (Campinas, 1996), 375-385, Lecture Notes in Pure and Appl. Math., 199, Dekker, New York, 1998.
   MR1655670
10. M. Álvarez de Morales, T. E. Pérez, M. A. Piñar, A. Ronveaux, Orthogonal polynomials associated with a nondiagonal Sobolev inner product with polynomial coefficients. Orthogonal functions, moment theory, and continued fractions (Campinas, 1996), 343-358, Lecture Notes in Pure and Appl. Math., 199, Dekker, New York, 1998.
    MR1655668
11. A. Martínez-Finkelshtein, J. J. Moreno-Balcázar, T. E. Pérez, M. A. Piñar, Asymptotics of Sobolev orthogonal polynomials for coherent pairs of measures. J. Approx. Theory 92 (1998), no. 2, 280-293.
    MR1604939
12. F. Marcellán, H. G. Meijer, T. E. Pérez, M. A. Piñar, An asymptotic result for Laguerre-Sobolev orthogonal polynomials. J. Comput. Appl. Math. 87 (1997), no. 1, 87-94.
    MR1488822
13. T. E. Pérez, M. A. Piñar, On Sobolev orthogonality for the generalized Laguerre polynomials. J. Approx. Theory 86 (1996), no. 3, 278-285.
    MR1405981
14. F. Marcellán, T. E. Pérez, M. A. Piñar, Laguerre-Sobolev orthogonal polynomials. J. Comput. Appl. Math. 71 (1996), no. 2, 245-265.
    MR1399895
15. F. Marcellán, T. E. Pérez, M. A. Piñar, A. Ronveaux, General Sobolev orthogonal polynomials. J. Math. Anal. Appl. 200 (1996), no. 3, 614-634.
    MR1393104

1991-1995

1. F. Marcellán, J. C. Petronilho, T. E. Pérez, M. A. Piñar, What is beyond coherent pairs of orthogonal polynomials? J. Comput. Appl. Math. 65 (1995), no. 1-3, 267-277.
   MR1379136
2. F. Marcellán, T. E. Pérez, M. A. Piñar, Regular Sobolev type orthogonal polynomials: the Bessel case. Rocky Mountain J. Math. 25 (1995), no. 4, 1431-1457.
   MR1371348
3. F. Marcellán, T. E. Pérez, M. A. Piñar, Orthogonal polynomials on weighted Sobolev spaces: the semiclassical case. Special functions (Torino, 1993). Ann. Numer. Math. 2 (1995), no. 1-4, 93-122.
   MR1343524
4. F. Marcellán, T. E. Pérez, M. A. Piñar, Gegenbauer-Sobolev orthogonal polynomials. Nonlinear numerical methods and rational approximation, II (Wilrijk, 1993), 71-82, Math. Appl., 296, Kluwer Acad. Publ., Dordrecht, 1994.
   MR1307190
5. T. E. Pérez, M. A. Piñar, Global properties of zeros for Sobolev-type orthogonal polynomials. J. Comput. Appl. Math. 49 (1993), no. 1-3, 225-232.
   MR1256030
6. M. A. Piñar, T. E. Pérez, On higher order Padé-type approximants with some prescribed coefficients in the numerator. Numer. Algorithms 3 (1992), no. 1-4, 345-352.
   MR1199381
7. F. Marcellán, T. E. Pérez, M. A. Piñar, On zeros of Sobolev-type orthogonal polynomials. Rend. Mat. Appl. (7) 12 (1992), no. 2, 455-473.
   MR1185903
8. T. Pérez Fernández, M. Piñar González, Properties of the Bernstein-Jacobi operator in Cr[0,1]. (Spanish) Proceedings of the XVth Portuguese-Spanish Conference on Mathematics, Vol. V (Portuguese) (Évora, 1990), 143-148, Univ. Évora, Évora, 1991.
   MR1161874

Other Publications (in Spanish)

• T. E. Pérez, De Jornadas, Congresos, Mujeres y Matemáticas. Boletín de la Titulación de Matemáticas de la UAL XI (2018), vol. 3, pág. 17-18 (publicacion digital).
  
• C. Aparicio del Prado, P. Martínez Amores, J. F. Mena Jurado, T. E. Pérez, Breve historia de la Sección. Matemáticas. 50 años en la Universidad de Granada, 11-15, Comisión Docente del Grado en Matemáticas. Granada, 2014.
• T. E. Pérez, Cincuenta años: cinco planes. Matemáticas. 50 años en la Universidad de Granada, 101-119, Comisión Docente del Grado en Matemáticas. Granada, 2014.
• T. E. Pérez, E. Santos Aláez, R. Raya Prida, MIT: Mujeres en la Informática y la Telecomunicación. Matematicalia 5 (2009), vol. 3 (publicacion digital).
  
• T. E. Pérez, E. Santos Aláez, R. Raya Prida, ¿Hay mujeres en los estudios de Informática y la Telecomunicación? Boletín de la Titulación de Matemáticas de la UAL III (2010), vol. 3, pág. 11-12 (publicacion digital).
  

Editorial Activity

• Reviewer for the American Mathematical Society
• Referee for the following Journals
  • Asymptotic Analysis
  • Bulletin of the Belgian Mathematical Society
  • Integral Transforms and Special Functions
  • Journal of Applied Analysis
  • Journal of Computational and Applied Mathematics
  • La Gaceta de la Real Sociedad Matemática Española
  • Linear and Multilinear Algebra
  • Mediterranean Journal of Mathematics
  • Methods and Applications of Analysis
  • Numerical Algorithms
  • Proceedings of the American Mathematical Society
  • The Ramanujan Journal
  • Results in Mathematics
  • SIGMA. Symmetry, Integrability, and Geometry: Methods and Applications

Dissemination

• MatEduca Project
  Dissemination Project designed to show the research activity at IMAG, the Institute of Mathematics at the University of Granada. It offers activities aimed at secondary school students, with the goal of highlighting the value of mathematical research. On June 6, 2025, the MatEduca project received the UGR award for Scientific Dissemination, call 2024.
• Conference: Zernike polynomials: orthogonality to the rescue of Optics.
  Annual National Congress of Students of Mathematics (ENEM 2025). Granada (Spain), July 22 - 27, 2025.
• Conference: Out of sight, out of mind... Math to the rescue!
  Sciences Week at the Sciences Faculty of the University of Granada. November 13, 2023.
• Women in Computer and Telecommunication. Virtual Exhibition in Divulgamat, 2009.

Researching

• Researching at Oberwolfach MFO. July, 2019.

Open problems

• My family. Barranco de la Luna (Granada). August, 2018.

Teaching

• Current academic year

Research

• Profiles
• Research Subjects
• Research Projects
• Publications
• Editorial Activity
• Dissemination
• Researching
• Open problems