Education
- Ph. D. (Mathematics), University Carlos III of Madrid
(Spain) 2012
- M. Sc. (Mathematical Engineering), University Carlos III
of Madrid, 2010
Current teaching
- Orthogonal Polynomials and Special Functions, PhD Program in Mathematics, University of Cádiz
Conferences/seminars currently being organized
- Seminars
of the Portuguese Group of Orthogonal Polynomials and
Special Functions (monthly)
- Portuguese-Polish Online Analysis Seminars (monthly)
- Orthogonal
Polynomials, Special Functions and their Applications,
Special Session of the International Conference on
Mathematical Analysis and Applications in Science and
Engineering, Porto, 20-22 June 2024
- From Classical to Modern Analysis: In memory of José Carlos Petronilho, Satellite Conference of the 9th European Mathematical Congress, Sanlúcar de Barrameda (Cádiz, Spain), 24-28 June 2024
Editorial Activity
Integral
Transform and Special Functions (Impact Factor 1.0, Q2)
(Editorial board)
Ph.D. students
- G.
Gordillo-Núñez, University of Coimbra (ongoing,
financed by FCT)
- A. Suzuki, University of Coimbra (ongoing, financed by FCT)
- J.
Rivero-Dones, University of Cádiz (May
2024, co-supervisor: M.
Villegas-Vallecillos)
- D. Mbouna, University of Coimbra (March 2021, advisor: J. Petronilho)
Papers
- K. Castillo, G. Filipuk and D. Mbouna, On classical
orthogonal polynomials on bi-lattices, arXiv.
- K. Castillo and D. Mbouna, Epilegomena to
the study of semiclassical orthogonal polynomials, arXiv.
- 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 (2023)
Article number: 155.
- 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, 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.
Others
- 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.