Castillo, Kenier; de Souza Costa, Marisa; Rafaeli, Fernando Rodrigo A survey on Markov’s theorem on zeros of orthogonal polynomials. (English) Zbl 1476.33006 Rassias, Themistocles M. (ed.) et al., Nonlinear analysis and global optimization. Cham: Springer. Springer Optim. Appl. 167, 23-50 (2021). MSC: 33C45 30C15 PDFBibTeX XMLCite \textit{K. Castillo} et al., Springer Optim. Appl. 167, 23--50 (2021; Zbl 1476.33006) Full Text: DOI
Castillo, Kenier; Souza Costa, Marisa de; Rafaeli, Fernando Rodrigo On zeros of polynomials in best \(L^p\)-approximation and inserting mass points. (English) Zbl 1469.30008 São Paulo J. Math. Sci. 15, No. 1, 485-492 (2021). MSC: 30C10 30C15 PDFBibTeX XMLCite \textit{K. Castillo} et al., São Paulo J. Math. Sci. 15, No. 1, 485--492 (2021; Zbl 1469.30008) Full Text: DOI arXiv
Castillo, K.; Rafaeli, F. R.; Suzuki, A. Stieltjes’ theorem for classical discrete orthogonal polynomials. (English) Zbl 1454.33009 J. Math. Phys. 61, No. 10, 103505, 16 p. (2020). MSC: 33C45 33E30 PDFBibTeX XMLCite \textit{K. Castillo} et al., J. Math. Phys. 61, No. 10, 103505, 16 p. (2020; Zbl 1454.33009) Full Text: DOI arXiv
Castillo, K.; Costa, M. S.; Rafaeli, F. R. On Markov’s theorem on zeros of orthogonal polynomials revisited. (English) Zbl 1428.33021 Appl. Math. Comput. 339, 390-397 (2018). MSC: 33C45 42C05 PDFBibTeX XMLCite \textit{K. Castillo} et al., Appl. Math. Comput. 339, 390--397 (2018; Zbl 1428.33021) Full Text: DOI
Borrego-Morell, J.; Rafaeli, F. R. An asymptotic expansion for a class of biorthogonal polynomials with respect to a measure on the unit circle. (English) Zbl 1426.42021 Appl. Math. Comput. 313, 52-73 (2017). MSC: 42C05 41A60 PDFBibTeX XMLCite \textit{J. Borrego-Morell} and \textit{F. R. Rafaeli}, Appl. Math. Comput. 313, 52--73 (2017; Zbl 1426.42021) Full Text: DOI
Borrego-Morell, J.; Rafaeli, Fernando Rodrigo On a class of biorthogonal polynomials on the unit circle. (English) Zbl 1342.33017 J. Math. Anal. Appl. 438, No. 1, 465-473 (2016). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 33C45 30E15 33C05 41A60 PDFBibTeX XMLCite \textit{J. Borrego-Morell} and \textit{F. R. Rafaeli}, J. Math. Anal. Appl. 438, No. 1, 465--473 (2016; Zbl 1342.33017) Full Text: DOI arXiv
Castillo, Kenier; Rafaeli, Fernando R. On the discrete extension of Markov’s theorem on monotonicity of zeros. (English) Zbl 1333.33013 ETNA, Electron. Trans. Numer. Anal. 44, 271-280 (2015). Reviewer: Chrysoula G. Kokologiannaki (Patras) MSC: 33C45 30C15 PDFBibTeX XMLCite \textit{K. Castillo} and \textit{F. R. Rafaeli}, ETNA, Electron. Trans. Numer. Anal. 44, 271--280 (2015; Zbl 1333.33013) Full Text: EMIS
Lun, Yen Chi; Rafaeli, Fernando Rodrigo Inequalities for zeros of Jacobi polynomials via Sturm’s theorem: Gautschi’s conjectures. (English) Zbl 1306.33020 Numer. Algorithms 67, No. 3, 549-563 (2014). Reviewer: Chrysoula G. Kokologiannaki (Patras) MSC: 33C45 34C10 PDFBibTeX XMLCite \textit{Y. C. Lun} and \textit{F. R. Rafaeli}, Numer. Algorithms 67, No. 3, 549--563 (2014; Zbl 1306.33020) Full Text: DOI
Castillo, K.; Dimitrov, D. K.; Garza, L. E.; Rafaeli, F. R. Perturbations on the antidiagonals of Hankel matrices. (English) Zbl 1329.15057 Appl. Math. Comput. 221, 444-452 (2013). MSC: 15B05 PDFBibTeX XMLCite \textit{K. Castillo} et al., Appl. Math. Comput. 221, 444--452 (2013; Zbl 1329.15057) Full Text: DOI Link
Dimitrov, Dimitar K.; Ismail, Mourad E. H.; Rafaeli, Fernando R. Interlacing of zeros of orthogonal polynomials under modification of the measure. (English) Zbl 1337.30003 J. Approx. Theory 175, 64-76 (2013). Reviewer: Fahreddin Abdullayev (Mersin) MSC: 30C10 30C15 33C45 PDFBibTeX XMLCite \textit{D. K. Dimitrov} et al., J. Approx. Theory 175, 64--76 (2013; Zbl 1337.30003) Full Text: DOI
Linhares de Andrade, Eliana Xavier; Bracciali, Cleonice Fátima; Rafaeli, Fernando Rodrigo Introduction to orthogonal polynomials. (Introdução aos polinômios ortogonais.) (Portuguese) Zbl 1481.33001 Notas em Matemática Aplicada 64. São Carlos: Sociedade Brasileira de Matemática Aplicada e Computacional (ISBN 978-85-8215-015-3/ebook). 144 p., open access (2012). MSC: 33-01 33C45 33C47 33C50 33C52 PDFBibTeX XMLCite \textit{E. X. Linhares de Andrade} et al., Introdução aos polinômios ortogonais (Portuguese). São Carlos: Sociedade Brasileira de Matemática Aplicada e Computacional (2012; Zbl 1481.33001) Full Text: Link
Castillo, Kenier; Lamblém, Regina Litz; Rafaeli, Fernando Rodrigo; Sri Ranga, Alagacone Szegő and para-orthogonal polynomials on the real line: zeros and canonical spectral transformations. (English) Zbl 1269.42016 Math. Comput. 81, No. 280, 2229-2249 (2012). MSC: 42C05 30B70 30E05 PDFBibTeX XMLCite \textit{K. Castillo} et al., Math. Comput. 81, No. 280, 2229--2249 (2012; Zbl 1269.42016) Full Text: DOI
Castillo, Kenier; Mello, Mirela V.; Rafaeli, Fernando R. Monotonicity and asymptotics of zeros of Sobolev type orthogonal polynomials: A general case. (English) Zbl 1256.33005 Appl. Numer. Math. 62, No. 11, 1663-1671 (2012). MSC: 33C45 42C05 PDFBibTeX XMLCite \textit{K. Castillo} et al., Appl. Numer. Math. 62, No. 11, 1663--1671 (2012; Zbl 1256.33005) Full Text: DOI
Huertas, Edmundo J.; Marcellán, Francisco; Rafaeli, Fernando R. Zeros of orthogonal polynomials generated by canonical perturbations of measures. (English) Zbl 1246.33004 Appl. Math. Comput. 218, No. 13, 7109-7127 (2012). MSC: 33C45 33C52 PDFBibTeX XMLCite \textit{E. J. Huertas} et al., Appl. Math. Comput. 218, No. 13, 7109--7127 (2012; Zbl 1246.33004) Full Text: DOI
Area, Iván; Dimitrov, Dimitar K.; Godoy, Eduardo; Rafaeli, Fernando R. Inequalities for zeros of Jacobi polynomials via Obrechkoff’s theorem. (English) Zbl 1247.33013 Math. Comput. 81, No. 278, 991-1004 (2012). Reviewer: Stamatis Koumandos (Nicosia) MSC: 33C45 26C10 PDFBibTeX XMLCite \textit{I. Area} et al., Math. Comput. 81, No. 278, 991--1004 (2012; Zbl 1247.33013) Full Text: DOI
Marcellán, Francisco; Rafaeli, Fernando R. Monotonicity and asymptotics of zeros of Laguerre-Sobolev-type orthogonal polynomials of higher order derivatives. (English) Zbl 1242.42021 Proc. Am. Math. Soc. 139, No. 11, 3929-3936 (2011). Reviewer: Andrei Martínez Finkelshtein (Almeria) MSC: 42C05 33C47 PDFBibTeX XMLCite \textit{F. Marcellán} and \textit{F. R. Rafaeli}, Proc. Am. Math. Soc. 139, No. 11, 3929--3936 (2011; Zbl 1242.42021) Full Text: DOI
Marcellán, Francisco; Rafaeli, Fernando R. A note on monotonicity of zeros of generalized Hermite-Sobolev-type orthogonal polynomials. (English) Zbl 1205.42026 Integral Transforms Spec. Funct. 21, No. 11-12, 831-838 (2010). MSC: 42C05 PDFBibTeX XMLCite \textit{F. Marcellán} and \textit{F. R. Rafaeli}, Integral Transforms Spec. Funct. 21, No. 11--12, 831--838 (2010; Zbl 1205.42026) Full Text: DOI
Dimitrov, Dimitar K.; Marcellán, Francisco; Rafaeli, Fernando R. Monotonicity of zeros of Laguerre-Sobolev-type orthogonal polynomials. (English) Zbl 1202.33015 J. Math. Anal. Appl. 368, No. 1, 80-89 (2010). Reviewer: Chrysoula G. Kokologiannaki (Patras) MSC: 33C45 42C05 34E05 PDFBibTeX XMLCite \textit{D. K. Dimitrov} et al., J. Math. Anal. Appl. 368, No. 1, 80--89 (2010; Zbl 1202.33015) Full Text: DOI
Dimitrov, Dimitar K.; Mello, Mirela V.; Rafaeli, Fernando R. Monotonicity of zeros of Jacobi-Sobolev type orthogonal polynomials. (English) Zbl 1191.33003 Appl. Numer. Math. 60, No. 3, 263-276 (2010). MSC: 33C45 42C05 PDFBibTeX XMLCite \textit{D. K. Dimitrov} et al., Appl. Numer. Math. 60, No. 3, 263--276 (2010; Zbl 1191.33003) Full Text: DOI
Huertas, Edmundo J.; Marcellán, Francisco; Rafaeli, Fernando R. Zeros of Orthogonal Polynomials Generated by Canonical Perturbations on Standard Measure. arXiv:1005.0336 Preprint, arXiv:1005.0336 [math.CA] (2010). MSC: 30C15 BibTeX Cite \textit{E. J. Huertas} et al., ``Zeros of Orthogonal Polynomials Generated by Canonical Perturbations on Standard Measure'', Preprint, arXiv:1005.0336 [math.CA] (2010) Full Text: arXiv OA License
Dimitrov, Dimitar K.; Rafaeli, Fernando R. Descartes rule of signs for orthogonal polynomials. (English) Zbl 1325.33008 East J. Approx. 15, No. 2, 233-262 (2009). MSC: 33C45 26C10 33C90 42C05 PDFBibTeX XMLCite \textit{D. K. Dimitrov} and \textit{F. R. Rafaeli}, East J. Approx. 15, No. 2, 233--262 (2009; Zbl 1325.33008)
Dimitrov, Dimitar K.; Rafaeli, Fernando R. Monotonicity of zeros of Laguerre polynomials. (English) Zbl 1181.33010 J. Comput. Appl. Math. 233, No. 3, 699-702 (2009). Reviewer: Alicia Cachafeiro López (Vigo) MSC: 33C45 33C47 42C05 PDFBibTeX XMLCite \textit{D. K. Dimitrov} and \textit{F. R. Rafaeli}, J. Comput. Appl. Math. 233, No. 3, 699--702 (2009; Zbl 1181.33010) Full Text: DOI
Dimitrov, Dimitar K.; Rafaeli, Fernando R. Monotonicity of zeros of Jacobi polynomials. (English) Zbl 1139.33003 J. Approx. Theory 149, No. 1, 15-29 (2007). Reviewer: Leonid Golinskii (Kharkov) MSC: 33C45 42C05 PDFBibTeX XMLCite \textit{D. K. Dimitrov} and \textit{F. R. Rafaeli}, J. Approx. Theory 149, No. 1, 15--29 (2007; Zbl 1139.33003) Full Text: DOI Link