Conferences

Celebrating 25 Years of Academic Excellence in Portugal: A Tribute to Professor Semyon Yakubovich,  University of Porto, 3-5 July 2025.
(Chair of the Organizing Committee)

Monthly Seminars

Editorial Activity

Integral Transform and Special Functions
(Editorial board)

Journal of Mathematical Sciences

Call for papers: From Classical to Modern Analysis: In memory of José Carlos Petronilho.
(Guest Editor)

I decline all review requests with short deadlines, from journals requiring payment from authors, or those that breach the implicit boundaries of conflict of interest in peer review. This includes submissions from close collaborators, students, or researchers with whom I have personal disagreements or scientific divergences.

Current PhD students

A crucial career step in developing independence is the PhD period, during which students are trained by their supervisors to become independent researchers, Studies in Higher Education (2024).

•  G. Gordillo-Núñez, University of Coimbra. 

• G. Gordillo-Núñez, The Nikiforov-Uvarov method, arXiv.
  
• G. Gordillo-Núñez and A. Suzuki, On zeros of discrete paraorthogonal polynomials on the unit circle, to appear in Integral Transforms Spec. Funct.
• G. Gordillo-Núñez, R. Álvarez-Nodarse, and N. Quintero, The complete solution of the Schrondinger equation with the Rosen-Morse type via the Nikiforov-Uvarov method, Physica D, 458 (2024) 1-12.
• A. Suzuki, University of Coimbra. 

• D. Mbouna and A. Suzuki, On some semiclassical orthogonal polynomials on lattices, submitted.
• A. Suzuki, Sturm's comparison theorem for classical discrete orthogonal polynomials, Results Math., 79 (2024) Article number: 153.
• D. Mbouna and A. Suzuki, Some Appell-type orthogonal polynomials on lattices, Ramanujan J., 64 (2024) 807-822.
• D. Mbouna and A. Suzuki, On another characterization of Askey-Wilson polynomials, Results Math., 77 (2022) Article number: 148. 

Past PhD Students 

• J. Rivero-Dones, University of Cádiz, Spain, Sobresaliente Cum Laude, May 2024, advisor 2: M. Villegas-Vallecillos)

 Data Scientist, QUANT AI Lab, Madrid, Spain

• D. Mbouna, University of Coimbra, (Aprovado com Distinção e Louvor, March 2021, advisor 1: J. Petronilho)

  Assistant Professor, La Rochelle Université, La Rochelle, France

Higher Education 

K. Castillo, Narcissism in the scientific community: Interview with Bruno Lemaitre (illustrated by Catarina Sobral), Linhas Críticas, 30 (2024) e53916. (Portuguese, English)

Books

K. Castillo and J. Petronilho, A First Course on Orthogonal Polynomials: Classical Orthogonal Polynomials and Related Topics, CRC Press, Chapman & Hall, New York, 2024. Designed cover image: Catarina Sobral (Portuguese National Illustration Award 2024).

I have waived any material benefits from this publication and relinquished all rights to support Research4Life.

Papers

• K. Castillo and G. Gordillo-Núñez, The multiple Markov theorem on Angelesco sets, arXiv.
  
• K. Castillo, On the product of the extreme zeros of Laguerre polynomials, arXix.
  
• K. Castillo and A. Suzuki, On the extension for Toeplitz matrices of certain Markov inequalities, arXiv.
  
• K. Castillo and D. Mbouna, Epilegomena to the study of semiclassical orthogonal polynomials, arXiv.
• K. Castillo, G. Filipuk and D. Mbouna, On classical orthogonal polynomials on bi-lattices, Anal. Math. Phys., 15, 25 (2025).
  
• K. Castillo and D. Mbouna, On a conjecture involving Askey-Wilson polynomials, to appear in Integral Transforms Spec. Funct.
• K. Castillo and D. Mbouna, A counterexample to a conjecture of M. Ismail, J. Math. Phys., 65 (2024) 033507.
  
• K. Castillo, C. M. da Fonseca and J. Petronilho, On Chebyshev polynomials and the inertia of certain tridiagonal matrices, Appl. Math. Comput., 467 (2024) 128497.
• K. Castillo, On the positivity of a certain function related with the Digamma function, Ramanujan J., 63 (2024) 253-258. 
  
• K. Castillo and J. Petronilho, Classical orthogonal polynomials revisited, Results Math., 78, 155 (2023).
  
• K. Castillo and D. Mbouna, Proof of two conjectures on Askey-Wilson polynomials, Proc. Amer. Math. Soc., 151 (2023) 1655-1661.
• K. Castillo, Remarks on the eigenvalues of a tridiagonal matrix in biogeography, Appl. Math. Comput., 437 (2023) 127546.
• K. Castillo, Remark on the characteristic polynomial of sl(2, F): A corollary that Muir missed, São Paulo J. Math. Sci., 17 (2023) 511-514.
  
• K. Castillo, Remark on "When are all the zeros of a polynomial real and distinct?", São Paulo J. Math. Sci., 16 (2022) 1030-1031.
• R. Álvarez-Nodarse, K. Castillo, D. Mbouna and J. Petronilho, On discrete coherent pairs of measures, J. Differ. Equ. Appl., 28 (2022) 853-868.
• K. Castillo, D. Mbouna and J. Petronilho, On the functional equation for classical orthogonal polynomials on lattices, J. Math. Anal. Appl., 515 (2022) 126390.
• K. Castillo, D. Mbouna and J. Petronilho, A characterization of continuous q-Jacobi, Chebyshev of the first kind and Al-Salam Chihara polynomials, J. Math. Anal. Appl., 514 (2022) 126358.
  
• K. Castillo and I. Zaballa, On variation of eigenvalues of birth and death matrices and random walk matrices, Adv. Appl. Math., 139 (2022) 102360.
• K. Castillo, D. Mbouna and J. Petronilho, Remarks on Askey-Wilson polynomials and Meixner polynomials of the second kind, Ramanujan J., 58 (2022) 1159-1170.
• K. Castillo, Markov's theorem for weight functions on the unit circle, Constr. Approx., 55 (2022) 605-627.
• K. Castillo and I. Zaballa, On a formula of Thompson and McEnteggert for the adjugate matrix, Linear Algebra Appl., 634 (2022) 37-56.
• K. Castillo, M. S. Costa and F. R. Rafaeli, On zeros of polynomials in best Lp-approximation and inserting mass points, São Paulo J. Math. Sci., 15 (2021) 485-492.
• K. Castillo, M. N. de Jesus and J. Petronilho, A note on orthogonal polynomials described by Chebyshev polynomials, J. Math. Anal. Appl., 497 (2021) 124906.
• K. Castillo, M. N. de Jesus, F. Marcellán and J. Petronilho, Hq-semiclassical orthogonal polynomials via polynomial mappings, Ramanujan J., 54 (2021) 113-136.
  
• K. Castillo, F. R. Rafaeli and A. Suzuki, Stieltjes' theorem for classical discrete orthogonal polynomials, J. Math. Phys., 61 (2020) 103505.
• R. Álvarez-Nodarse, K. Castillo, D. Mbouna and J. Petronilho, On classical orthogonal polynomials related to Hahn’s operator, Integral Transforms Spec. Funct., 31 (2020) 487-505.
• K. Castillo, M. N. de Jesus and J. Petronilho, An electrostatic interpretation of the zeros of sieved ultraspherical polynomial, J. Math. Phys., 61 (2020) 053501.
• K. Castillo and D. Mbouna, On another extension of coherent pairs of measures, Indag. Math. (N.S.), 31 (2020) 223-234.
• K. Castillo, M. N. de Jesus and J. Petronilho, A proof of a conjecture  about a symmetric system of orthogonal polynomials, Integral Transforms Spec. Funct., 31 (2020) 299-303.
• K. Castillo, On monotonicity of zeros of paraorthogonal polynomials on the unit circle, Linear Algebra Appl., 580 (2019) 474-490.
• K. Castillo and J. Petronilho, Refined interlacing properties for zeros of paraorthogonal polynomials on the unit circle, Proc. Amer. Math. Soc., 146 (2018) 3285-3294.
• K. Castillo, M. S. Costa and F. R. Rafaeli, On Markov's theorem on zeros of orthogonal polynomials revisited, Appl. Math. Comput., 339 (2018) 390-397.
• K. Castillo, M. N. de Jesus and J. Petronilho, On semiclassical orthogonal polynomials via polynomial mappings, J. Math. Anal. Appl., 455 (2017) 1801-1821.
• K. Castillo and M. N. Rebocho, On linear spectral transformations and the Laguerre-Hahn class, Integral Transforms Spec. Funct., 28 (2017) 859-875.
• K. Castillo, F. Marcellán and J. Rivero, On perturbed orthogonal polynomials on the real line and the unit circle via Szegő's transformation, Appl. Math. Comput., 302 (2017) 97-110.
• K. Castillo, R. Cruz-Barroso and F. Perdomo-Pío, On a spectral theorem in para-orthogonality theory, Pacific J. Math., 280 (2016) 71-91.
• K. Castillo and F. R. Rafaeli, A short note on interlacing and monotonicity of zeros of orthogonal polynomial, AIP Conf. Proc., 1776 (2016) 090004.
• K. Castillo, F. Marcellán and M. N. Rebocho, Zeros of para-orthogonal polynomials and linear spectral transformations on the unit circle, Numer. Algorithms, 71 (2016) 699-714.
• K. Castillo, Monotonicity of zeros for a class of polynomials including hypergeometric polynomials, Appl. Math. Comput., 266 (2015) 183-193.
• K. Castillo and F. R. Rafaeli, On the discrete extension of Markov's theorem on monotonicity of zeros, Electron. Trans. Numer. Anal., 44 (2015) 271-280.
• K. Castillo, F. Marcellán and J. Rivero, On co-polynomials on the real line, J. Math. Anal. Appl., 427 (2015) 469-483.
• K. Castillo, On perturbed Szegő recurrences, J. Math. Anal. Appl., 411 (2014) 742-752.
• K. Castillo, M. S. Costa, A. Sri Ranga and D. O. Veronese, A Favard type theorem for orthogonal polynomials on the unit circle from a three-term recurrence formula, J. Approx. Theory, 184 (2014) 146-162.
• K. Castillo, L. G. Garza and F. Marcellán, On computational aspects of discrete Sobolev inner products, Appl. Math. Comput., 223 (2013) 452-460.
• K. Castillo, D. K. Dimitrov, L. E. Garza and F. R. Rafaeli, Perturbations on the antidiagonals of Hankel matrices, Appl. Math. Comput., 221 (2013) 444-452.
• K. Castillo, L. E. Garza and F. Marcellán, Asymptotic behaviour of Sobolev orthogonal polynomials on the unit circle, Integral Transforms Spec. Funct., 24 (2013) 23-38.
• K. Castillo and F. Marcellán, Generators of rational spectral transformations for nontrivial C-functions, Math. Comp., 82 (2013) 1197-1221.
• K. Castillo, R. L. Lamblem and A. Sri. Ranga, On a moment problem associated with Chebyshev polynomials, Appl. Math. Comput., 218 (2012) 9571-9574.
• K. Castillo, M. V. Mello and F. R. Rafaeli, Monotonicity and asymptotics of zeros of Sobolev type orthogonal polynomials: A general case, Appl. Numer. Math., 62 (2012) 1663-1671.
• K. Castillo, A new approach to relative asymptotic behavior for discrete Sobolev-type orthogonal polynomials on the unit circle, Appl. Math. Lett., 25 (2012) 1000-1004.
• K. Castillo, R. L. Lamblen, A. Sri Ranga and F. R. Rafaeli, Szegő polynomials and para-orthogonal polynomials on the real line. Zeros and canonical spectral transformations, Math. Comp., 81 (2012) 2229-2249.
• K. Castillo, L. E. Garza and F. Marcellán, Zeros of Sobolev orthogonal polynomials on the unit circle, Numer. Algorithms, 60 (2012) 669-681.
• K. Castillo, L. E. Garza and F. Marcellán, A new linear spectral transformation associated with derivatives of Dirac linear functionals, J. Approx. Theory, 163 (2011) 1834-1853.
• K. Castillo, L. E. Garza and F. Marcellán, Perturbations on the subdiagonals of Toeplitz matrices, Linear Algebra Appl., 434 (2011) 1563-1579.
• K. Castillo, L. E. Garza and F. Marcellán, Laurent polynomials perturbations of linear functional. An inverse problem, Electron. Trans. Numer. Anal., 36 (2010) 83-98.
• K. Castillo, L. E. Garza and F. Marcellán, Linear spectral transformations, Hessenberg matrices and orthogonal polynomials, Rend. Circ. Mat. Palermo, 82 (2010) 3-26.

Book chapters

• K. Castillo, D. Mbouna and J. Petronilho, On classical orthogonal polynomials on lattices and some characterization theorems (P. M. Pardalos and Th. M. Rassias, eds.), Mathematical Analysis, Optimization, Approximation and Applications, World Scientific, Singapore (2025) 157-183
  
• K. Castillo, M. S. Costa and F. R. Rafaeli, A survey on Markov's theorem on zeros of orthogonal polynomials (Th. M. Rassias and P. M. Pardalos, eds.), Series: Springer Optimization and its Applications, Springer Verlag, Berlin-Heidelberg-New York (2021) 23-50.
• K. Castillo, F. Marcellán and J. Rivero, On co-polynomials on the real line and the unit circle (N. Daras and Th. M. Rassias, eds.), Series: Springer Optimization and its Applications, Springer Verlag, Berlin-Heidelberg-New York (2017) 69-94.
• K. Castillo and F. Marcellán, On some recent results on asymptotic behavior of orthogonal polynomials on the unit circle and inserting point masses (N. Daras and M. Th. Rassias, eds.), Series: Springer Optimization and its Applications, Springer Verlag, Berlin-Heidelberg-New York (2015) 75-102.
• K. Castillo, L. E. Garza and F. Marcellán, On a direct Uvarov-Chihara problem and some extensions (K. Alladi, G. V. Milovanovic and M. Th. Rassias, eds.), Series: Springer Optimization and its Applications, Springer Verlag, Berlin-Heidelberg-New York (2014) 691-704.

Edited Books

Popularization

• K. Castillo and Z. da Rocha, A história de uma parceria. Entrevista com Claude Brezinski e Michela Redivo-Zaglia, Gazeta Matemática, 189 (2020) 34-43.
• K. Castillo and Z. da Rocha, Uma ideia natural funciona sempre. Uma entrevista com Pascal Maroni, Gazeta de Matemática, 187 (2019) 24-30.