Renato Alvarez-Nodarse

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Updated:

April 9, 2025



      




Links of interest

Renato Álvarez-Nodarse's Publications

 Google Scholar profile  ORCID profile Research ID (WoS) Prisma


[Preprints]   [Papers]  [Edited Volumes]  [Contributions in Proceedings and books

[Papers on the COVID19]  [Books]  [Others]  [Divulgación] [Charlas]  [Meetings


Preprints

  1. R. Alvarez-Nodarse, A. Arenas-Gomez. On the quantum algebra suq(1,1) from a Special Function standpoint. (2025) arXiv:2507.14100 [math-ph]

  2. Renato Alvarez-Nodarse and Kenier Castilla, A Note on the Paper "Localization of Zeros of Polar Polynomials on the Unit Disk". (2025) arXiv:2510.01703 [math.CA]

Research papers

[2025]  [2024]  [2023]  [2022]  [2021]  [2020]  [2019

[2015]  [2014]  [2013]  [2012]  [2011]  [2010]  [2009]  [2007]  [2006]  [2005

[2004]  [2003]  [2002]  [2001]  [1999]  [1998]  [1997]  [1996]  [1995]  [1994]



    Edited Volumes:

  1. Special Volume of the Electronic Transactions on Numerical Analysis (ETNA) Orthogonal Polynomials and Mathematical Physics. ETNA 24, 2006 R. Álvarez-Nodarse, J. Arvesú, and F. Marcellán (Invited Eds.). Proceedings of the IWOP04
     
  2. Special Volume of the Electronic Transactions on Numerical Analysis (ETNA) on Orthogonal Polynomials in Approximation Theory. ETNA 19, 2005 R. Álvarez-Nodarse, J. Arvesú, and F. Marcellán (Invited Eds.). Proceedings of the IWOP02
     
  3. Laredo Lecture Notes (Lecture notes of the 1st SIAG Summer School on Orthogonal Polynomials and Special Functions, Laredo, Spain, July 24-29 2000). Nova Science Publisher (2004). R. Álvarez-Nodarse, F. Marcellán and W. Van Assche (Eds.). 2004 ISBN: 1-59454-09-8.
     
  4. Special Volume of the Electronic Transactions on Numerical Analysis (ETNA) on Orthogonal Polynomials: Numerical and Symbolic Algorithms. ETNA 9, 1999 R. Álvarez-Nodarse and F. Marcellán (Invited Eds.). Proceedings of the IWOP98
     
  5. Proceedings of the International Workshop on Orthogonal Polynomials on Mathematical Physics. M. Alfaro, R. Álvarez-Nodarse, G. López Lagomasino, and F. Marcellán Eds. Servicio de Publicaciones de la Universidad Carlos III de Madrid. Leganés, Madrid (1997). This monography is free avaliable from this site.

    Contributions to Proceedings and books

  1. R. Álvarez-Nodarse. Los q-polinomios hipergeométricos . In: Margarita Matemática. En honor de José Javier Guadalupe ``Chicho''. L. Español y J.L. Varona Eds. Servicio de Publicaciones, Universidad de La Rioja, Logroño, Spain, 2001, pp 85-96.
     
  2. R. Álvarez-Nodarse y Antonio J. Duran: Polinomios ortogonales. In: Actas del Encuentro de Matemáticos Andaluces. Universidad de Sevilla E. Briales Morales, A. Carriazo Rubio, T. Chacón, P. Real Jurado y A. Romero Jiménez Eds. Universidad de Sevilla, Secretariado de Publicaciones, (2001), pp. 25-42.
     
  3. R. Álvarez-Nodarse, F. Marcellán and J. Petronilho: On Some Polynomial Mappings for Measures. Applications. . (1996) In: Proceedings of the International Workshop on Orthogonal Polynomials on Mathematical Physics. M. Alfaro, R. Álvarez-Nodarse, G. López Lagomasino, and F. Marcellán Eds. Leganés, Madrid (1997), 1-22. MA/UC3M/29/1996
     
  4. R. Álvarez-Nodarse and Yu. F. Smirnov: The dual Hahn q-Polynomials in the lattice x(s) = [s]q [s+1]q and the q-algebras q-SU(1,1) and q-SU(2).(revised version October 1996) . In: Proceedings of Fourth Wigner Symposium N.Atakishiev, T.H.Seligman and K.B.Wolf Eds. World Scientific, Singapore, (1996), 429-434.
     
  5. R. N. Alvarez, D. Bonatsos, and Yu.F. Smirnov: q-Deformed vibron model for diatomic molecules. In: Perspectives for the interacting boson model}. Proceedings of Padova conference. On the occasion of its 20th anniversary R.F. Casten, A. Vitturi, A.B. Balantekin, B.R. Barrett, J. N. Ginocchio, G. Maino and T. Otsuka (Eds.) World Scientific, (1994), 575-589.

Books:

  • R. Álvarez-Nodarse. Polinomios hipergemétricos y q-polinomios. Monografías del Seminario Matemático "García de Galdeano" Número 26. Prensas Universitarias de Zaragoza, Spain, 2003. ISBN 84-7733-637-7. 343 pages. Versión electrónica actualizada el 10 de noviembre de 2014.

  • J. Arvesú, R. Álvarez-Nodarse y F. Marcellán ``Álgebra Lineal y aplicaciones'' Editorial Síntesis, ISBN 84-7738-702-8. (for more information see the book Home Page.

  • R. Álvarez-Nodarse. Introducción a Maxima CAS con aplicaciones a la resolución de ecuaciones diferenciales ordinarias (updated at December 1st, 2017). This is a concise introductory course to the Computer Algebra System Maxima. The wxMaxima source files for each chapter are avaliable from HERE.

  • R. Álvarez-Nodarse. Breve introducción a la mecánica cuántica (updated at December 1st, 2017). This is the full text on some courses given at the Universidad de Zaragoza, Universidade de Coimbra and also at the FISMAT2015 in Sevilla in the Summer of 2015. It includes and introduction to the Quantum Mechanics on Hilbert Spaces, the classical orthogonal polynomials as well as two methods for solving the Schrödinger equation: the Nikiforov-Uvarov method and the Factorization method of E. Schrödinger.


Others:

  1. Ortogonalidad y aplicaciones. This is the updated notes (December 2023) of a course on the applications of orthogonal polynomials in the theory of random walks as well as in the resolution of the Schrödinger equation using the Nikiforov-Uvarov method. The course was given on November 2016 at the 1st ORTHONET School.


Some articles on science popularization

Here you can find the links to my articles on popular science. The links are to the Spanis original version of the works, but almost all of then have been transilated to English.

⚛   General Science

😷 On the COVID-19 pandemic

Charlas para un público general

 

📟  100 años de la mecánica cuántica: la teoría más desconcertante y revolucionaria que haya existido jamás (in Spanish) Charla de carácter divulgativo impartida el jueves 22 de mayo de 2025, Escuela de Infórmatica (Reina Mercedes) de la Universidad de Sevilla organizada Club Algoritmia (Click on the image)


 

📟  ¿Son las matemáticas el lenguaje de la naturaleza? (in Spanish) Charla de carácter divulgativo impartida el jueves 6 de marzo de 2025, Escuela de Infórmatica (Reina Mercedes) de la Universidad de Sevilla en el Club Algoritmia (Click on the image)


 

📟  Las Matemáticas ... y el mundo que nos rodea (in Spanish). Charla de carácter divulgativo impartida el viernes 7 de febrero de 2025 en el Pizza Seminar en la Facultad de Ciencia de la Universidad de Cadiz (Click on the image)


 

📟  Jose Carlos Petronilho: an outstanding mathematician and even better person (in English). Charla inaugural del Congreso "From Classical to Modern Analysis: In memory of Professor José Carlos Petronilho" a Satellite Conference of the 9th European Mathematical Congress, June 24-28, 2024, in Sanlúcar de Barrameda (Cadíz, Spain). (Click on the image)

 

 


Web pages of some meetings which I have co-organized


Site info: © 2009 Renato Álvarez-Nodarse