García-Ardila, Juan C.; Marcellán, Francisco; Marriaga, Misael E. From standard orthogonal polynomials to Sobolev orthogonal polynomials: the role of semiclassical linear functionals. (English) Zbl 1443.33013 Foupouagnigni, Mama (ed.) et al., Orthogonal polynomials. Proceedings of the 2nd AIMS-Volkswagen Stiftung workshop on introduction to orthogonal polynomials and applications, Douala, Cameroon, October 5–12, 2018. Cham: Birkhäuser. Tutor. Sch. Workshops Math. Sci., 245-292 (2020). MSC: 33C45 42C05 PDF BibTeX XML Cite \textit{J. C. García-Ardila} et al., in: Orthogonal polynomials. Proceedings of the 2nd AIMS-Volkswagen Stiftung workshop on introduction to orthogonal polynomials and applications, Douala, Cameroon, October 5--12, 2018. Cham: Birkhäuser. 245--292 (2020; Zbl 1443.33013) Full Text: DOI
Huertas, Edmundo J.; Soria-Lorente, Anier New analytic properties of nonstandard Sobolev-type Charlier orthogonal polynomials. (English) Zbl 1420.33003 Numer. Algorithms 82, No. 1, 41-68 (2019). MSC: 33C47 PDF BibTeX XML Cite \textit{E. J. Huertas} and \textit{A. Soria-Lorente}, Numer. Algorithms 82, No. 1, 41--68 (2019; Zbl 1420.33003) Full Text: DOI
Bobkov, Sergey G.; Götze, Friedrich; Sambale, Holger Higher order concentration of measure. (English) Zbl 1447.60049 Commun. Contemp. Math. 21, No. 3, Article ID 1850043, 36 p. (2019). Reviewer: Oleg K. Zakusilo (Kyïv) MSC: 60E15 60F10 41A10 41A80 PDF BibTeX XML Cite \textit{S. G. Bobkov} et al., Commun. Contemp. Math. 21, No. 3, Article ID 1850043, 36 p. (2019; Zbl 1447.60049) Full Text: DOI arXiv
Sharapudinov, Idris Idrisovich; Gadzhieva, Zul’fiya Dzhamaldinovna; Gadzhimirzaev, Ramis Makhmudovich Difference equations and Sobolev orthogonal polynomials, generated by Meixner polynomials. (Russian. English summary) Zbl 1450.39001 Vladikavkaz. Mat. Zh. 19, No. 2, 58-72 (2017). MSC: 39A12 33C45 PDF BibTeX XML Cite \textit{I. I. Sharapudinov} et al., Vladikavkaz. Mat. Zh. 19, No. 2, 58--72 (2017; Zbl 1450.39001) Full Text: MNR
Sharapudinov, I. I.; Sharapudinov, T. I. Polynomials orthogonal in the Sobolev sense, generated by Chebyshev polynomials orthogonal on a mesh. (English. Russian original) Zbl 1376.33015 Russ. Math. 61, No. 8, 59-70 (2017); translation from Izv. Vyssh. Uchebn. Zaved., Mat. No. 8, 67-79 (2017). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 33C45 42C05 PDF BibTeX XML Cite \textit{I. I. Sharapudinov} and \textit{T. I. Sharapudinov}, Russ. Math. 61, No. 8, 59--70 (2017; Zbl 1376.33015); translation from Izv. Vyssh. Uchebn. Zaved., Mat. No. 8, 67--79 (2017) Full Text: DOI
Sharapudinov, I. I.; Gadzhieva, Z. D. Sobolev orthogonal polynomials generated by Meixner polynomials. (Russian. English summary) Zbl 1355.42034 Izv. Sarat. Univ. (N.S.), Ser. Mat. Mekh. Inform. 16, No. 3, 310-321 (2016). MSC: 42C15 33C50 PDF BibTeX XML Cite \textit{I. I. Sharapudinov} and \textit{Z. D. Gadzhieva}, Izv. Sarat. Univ. (N.S.), Ser. Mat. Mekh. Inform. 16, No. 3, 310--321 (2016; Zbl 1355.42034) Full Text: DOI
Domínguez, V.; Ganesh, M. Sobolev estimates for constructive uniform-grid FFT interpolatory approximations of spherical functions. (English) Zbl 1347.42004 Adv. Comput. Math. 42, No. 4, 843-887 (2016). MSC: 42A15 42A10 42A38 65T40 65T50 65D32 33C55 PDF BibTeX XML Cite \textit{V. Domínguez} and \textit{M. Ganesh}, Adv. Comput. Math. 42, No. 4, 843--887 (2016; Zbl 1347.42004) Full Text: DOI
Ruzhansky, Michael; Tikhonov, Sergey Some problems in Fourier analysis and approximation theory. (English) Zbl 1343.42001 Ruzhansky, Michael (ed.) et al., Methods of Fourier analysis and approximation theory. Collected papers based on the presentations at the 9th ISAAC congress, section “Approximation theory and Fourier analysis”, Crakow, Poland, August 5–9, 2013 and at the conference on Fourier analysis and approximation theory in the CRM, Barcelona, Spain, November 4–8, 2013. Basel: Birkhäuser/Springer (ISBN 978-3-319-27465-2/hbk; 978-3-319-27466-9/ebook). Applied and Numerical Harmonic Analysis, 1-19 (2016). MSC: 42-02 41-02 49-02 42B20 42B10 42C15 42C10 42A99 42A10 41A17 49J40 49M25 32A35 32A22 46E35 26B05 65C05 PDF BibTeX XML Cite \textit{M. Ruzhansky} and \textit{S. Tikhonov}, in: Methods of Fourier analysis and approximation theory. Collected papers based on the presentations at the 9th ISAAC congress, section ``Approximation theory and Fourier analysis'', Crakow, Poland, August 5--9, 2013 and at the conference on Fourier analysis and approximation theory in the CRM, Barcelona, Spain, November 4--8, 2013. Basel: Birkhäuser/Springer. 1--19 (2016; Zbl 1343.42001) Full Text: DOI
Peña, A.; Rezola, M. L. Connection formulas for general discrete Sobolev polynomials: Mehler-Heine asymptotics. (English) Zbl 1410.42026 Appl. Math. Comput. 261, 216-230 (2015). MSC: 42C05 33C45 PDF BibTeX XML Cite \textit{A. Peña} and \textit{M. L. Rezola}, Appl. Math. Comput. 261, 216--230 (2015; Zbl 1410.42026) Full Text: DOI arXiv
Osilenker, B. P. On linear summability methods of Fourier series in polynomials orthogonal in a discrete Sobolev space. (English. Russian original) Zbl 1333.42050 Sib. Math. J. 56, No. 2, 339-351 (2015); translation from Sib. Mat. Zh. 56, No. 2, 420-435 (2015). Reviewer: Delfina Roux (Milano) MSC: 42C10 40C05 40G05 40G99 PDF BibTeX XML Cite \textit{B. P. Osilenker}, Sib. Math. J. 56, No. 2, 339--351 (2015; Zbl 1333.42050); translation from Sib. Mat. Zh. 56, No. 2, 420--435 (2015) Full Text: DOI
Durán, Antonio J.; de la Iglesia, Manuel D. Differential equations for discrete Laguerre-Sobolev orthogonal polynomials. (English) Zbl 1320.42018 J. Approx. Theory 195, 70-88 (2015). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 42C05 33C45 34A05 PDF BibTeX XML Cite \textit{A. J. Durán} and \textit{M. D. de la Iglesia}, J. Approx. Theory 195, 70--88 (2015; Zbl 1320.42018) Full Text: DOI arXiv
Robert, Didier; Thomann, Laurent Random weighted Sobolev inequalities and application to quantum ergodicity. (English) Zbl 1341.60074 Commun. Math. Phys. 335, No. 3, 1181-1209 (2015). MSC: 60H30 46E35 46E39 33C45 81Q05 PDF BibTeX XML Cite \textit{D. Robert} and \textit{L. Thomann}, Commun. Math. Phys. 335, No. 3, 1181--1209 (2015; Zbl 1341.60074) Full Text: DOI arXiv
Poiret, Aurélien; Robert, Didier; Thomann, Laurent Random-weighted Sobolev inequalities on \(\mathbb{R}^d\) and application to Hermite functions. (English) Zbl 1310.81060 Ann. Henri Poincaré 16, No. 2, 651-689 (2015). Reviewer: Michael Perelmuter (Kyïv) MSC: 81Q05 46E39 33C45 PDF BibTeX XML Cite \textit{A. Poiret} et al., Ann. Henri Poincaré 16, No. 2, 651--689 (2015; Zbl 1310.81060) Full Text: DOI
Huertas, Edmundo J.; Marcellán, Francisco; Pérez-Valero, M. Francisca; Quintana, Yamilet Asymptotics for Laguerre-Sobolev type orthogonal polynomials modified within their oscillatory regime. (English) Zbl 1334.33025 Appl. Math. Comput. 236, 260-272 (2014). MSC: 33C45 PDF BibTeX XML Cite \textit{E. J. Huertas} et al., Appl. Math. Comput. 236, 260--272 (2014; Zbl 1334.33025) Full Text: DOI
Castillo, Kenier; Garza, Lino G.; Marcellán, Francisco On computational aspects of discrete Sobolev inner products on the unit circle. (English) Zbl 1329.65086 Appl. Math. Comput. 223, 452-460 (2013). MSC: 65F30 33C45 42A16 65T40 PDF BibTeX XML Cite \textit{K. Castillo} et al., Appl. Math. Comput. 223, 452--460 (2013; Zbl 1329.65086) Full Text: DOI
Marcellán, Francisco; Zejnullahu, Ramadan; Fejzullahu, Bujar; Huertas, Edmundo On orthogonal polynomials with respect to certain discrete Sobolev inner product. (English) Zbl 1259.33023 Pac. J. Math. 257, No. 1, 167-188 (2012). Reviewer: Jaebum Sohn (Seoul) MSC: 33C47 42C05 PDF BibTeX XML Cite \textit{F. Marcellán} et al., Pac. J. Math. 257, No. 1, 167--188 (2012; Zbl 1259.33023) Full Text: DOI Link
Berriochoa, Elías; Cachafeiro, Alicia Algorithms for solving Hermite interpolation problems using the fast Fourier transform. (English) Zbl 1215.33009 J. Comput. Appl. Math. 235, No. 4, 882-894 (2010). Reviewer: Valery V. Karachik (Chelyabinsk) MSC: 33C47 65D05 33C52 65T50 65D15 65T40 PDF BibTeX XML Cite \textit{E. Berriochoa} and \textit{A. Cachafeiro}, J. Comput. Appl. Math. 235, No. 4, 882--894 (2010; Zbl 1215.33009) Full Text: DOI
Demkowicz, Leszek; Gopalakrishnan, Jayadeep; Schöberl, Joachim Polynomial extension operators. II. (English) Zbl 1208.46030 SIAM J. Numer. Anal. 47, No. 5, 3293-3324 (2009). Reviewer: Wilhelm Heinrichs (Essen) MSC: 46E35 46E39 65N30 47H60 11C08 31B10 PDF BibTeX XML Cite \textit{L. Demkowicz} et al., SIAM J. Numer. Anal. 47, No. 5, 3293--3324 (2009; Zbl 1208.46030) Full Text: DOI
Pesenson, Isaac Paley-Wiener approximations and multiscale approximations in Sobolev and Besov spaces on manifolds. (English) Zbl 1171.42016 J. Geom. Anal. 19, No. 2, 390-419 (2009). MSC: 42C05 41A17 41A65 43A85 46C99 PDF BibTeX XML Cite \textit{I. Pesenson}, J. Geom. Anal. 19, No. 2, 390--419 (2009; Zbl 1171.42016) Full Text: DOI
Costas-Santos, R. S.; Sánchez-Lara, J. F. Extensions of discrete classical orthogonal polynomials beyond the orthogonality. (English) Zbl 1167.42008 J. Comput. Appl. Math. 225, No. 2, 440-451 (2009). Reviewer: Alexei Lukashov (Istanbul) MSC: 42C05 33C45 PDF BibTeX XML Cite \textit{R. S. Costas-Santos} and \textit{J. F. Sánchez-Lara}, J. Comput. Appl. Math. 225, No. 2, 440--451 (2009; Zbl 1167.42008) Full Text: DOI arXiv arXiv
Nagai, Atsushi; Kametaka, Yoshinori; Yamagishi, Hiroyuki; Takemura, Kazuo; Watanabe, Kohtaro Discrete Bernoulli polynomials and the best constant of the discrete Sobolev inequality. (English) Zbl 1158.46026 Funkc. Ekvacioj, Ser. Int. 51, No. 2, 307-327 (2008). MSC: 46E39 11B68 26D15 PDF BibTeX XML Cite \textit{A. Nagai} et al., Funkc. Ekvacioj, Ser. Int. 51, No. 2, 307--327 (2008; Zbl 1158.46026) Full Text: DOI Link
Osilenker, B. P. An extremal problem for algebraic polynomials in the symmetric discrete Gegenbauer–Sobolev space. (English. Russian original) Zbl 1165.46014 Math. Notes 82, No. 3, 366-379 (2007); translation from Mat. Zametki 82, No. 3, 411-425 (2007). MSC: 46E39 33C45 PDF BibTeX XML Cite \textit{B. P. Osilenker}, Math. Notes 82, No. 3, 366--379 (2007; Zbl 1165.46014); translation from Mat. Zametki 82, No. 3, 411--425 (2007) Full Text: DOI
Escribano, C.; Sastre, M. A.; Torrano, E. Moment matrix of self-similar measures. (English) Zbl 1160.42308 ETNA, Electron. Trans. Numer. Anal. 24, 79-87 (2006). MSC: 42C05 28A80 60J05 PDF BibTeX XML Cite \textit{C. Escribano} et al., ETNA, Electron. Trans. Numer. Anal. 24, 79--87 (2006; Zbl 1160.42308) Full Text: Link EuDML
Marcellán, Francisco; Szafraniec, Franciszek Hugon Integral representations on equipotential and harmonic sets. (English) Zbl 1082.46026 Bull. Belg. Math. Soc. - Simon Stevin 11, No. 3, 457-468 (2004). Reviewer: Yang Dachun (Beijing) MSC: 46E35 46E39 46E20 43A35 44A60 30E05 47A57 PDF BibTeX XML Cite \textit{F. Marcellán} and \textit{F. H. Szafraniec}, Bull. Belg. Math. Soc. - Simon Stevin 11, No. 3, 457--468 (2004; Zbl 1082.46026) Full Text: Euclid
Kwon, K. H.; Lee, J. H.; Marcellán, F. Generalized \(\Delta\)-coherent pairs. (English) Zbl 1058.42018 J. Korean Math. Soc. 41, No. 6, 977-664 (2004). MSC: 42C05 33C45 PDF BibTeX XML Cite \textit{K. H. Kwon} et al., J. Korean Math. Soc. 41, No. 6, 977--664 (2004; Zbl 1058.42018) Full Text: DOI
Area, I.; Godoy, E.; Marcellán, F. \(\Delta\)-coherent pairs and orthogonal polynomials of a discrete variable. (English) Zbl 1047.42019 Integral Transforms Spec. Funct. 14, No. 1, 31-57 (2003). Reviewer: Andrei Martínez Finkelshtein (Almeria) MSC: 42C05 33C45 PDF BibTeX XML Cite \textit{I. Area} et al., Integral Transforms Spec. Funct. 14, No. 1, 31--57 (2003; Zbl 1047.42019) Full Text: DOI
Hendriks, Harrie Application of fast spherical Fourier transform to density estimation. (English) Zbl 1026.62033 J. Multivariate Anal. 84, No. 2, 209-221 (2003). MSC: 62G07 62H11 60E10 65T50 46E35 62G20 46N30 PDF BibTeX XML Cite \textit{H. Hendriks}, J. Multivariate Anal. 84, No. 2, 209--221 (2003; Zbl 1026.62033) Full Text: DOI
Marcellán, F.; Osilenker, B. P.; Rocha, I. A. On Fourier series of Jacobi-Sobolev orthogonal polynomials. (English) Zbl 1016.42014 J. Inequal. Appl. 7, No. 5, 673-699 (2002). MSC: 42C05 PDF BibTeX XML Cite \textit{F. Marcellán} et al., J. Inequal. Appl. 7, No. 5, 673--699 (2002; Zbl 1016.42014) Full Text: DOI EuDML
Marcellán, F.; Osilenker, B. P.; Rocha, I. A. On Fourier series of a discrete Jacobi–Sobolev inner product. (English) Zbl 1019.42014 J. Approximation Theory 117, No. 1, 1-22 (2002). MSC: 42C05 33C47 PDF BibTeX XML Cite \textit{F. Marcellán} et al., J. Approx. Theory 117, No. 1, 1--22 (2002; Zbl 1019.42014) Full Text: DOI
Branquinho, Amilcar; Foulquié Moreno, Ana; Marcellán, Francisco Asymptotic behavior of Sobolev-type orthogonal polynomials on a rectifiable Jordan curve or arc. (English) Zbl 0991.42018 Constr. Approx. 18, No. 2, 161-182 (2002). MSC: 42C05 PDF BibTeX XML Cite \textit{A. Branquinho} et al., Constr. Approx. 18, No. 2, 161--182 (2002; Zbl 0991.42018) Full Text: DOI
Álvarez de Morales, María; Pérez, Teresa E.; Pinar, Miguel A. Orthogonal polynomials associated with a \(\Delta\)-Sobolev inner product. (English) Zbl 0997.39007 J. Difference Equ. Appl. 8, No. 2, 125-151 (2002). MSC: 39A12 33C45 42C05 46C50 PDF BibTeX XML Cite \textit{M. Álvarez de Morales} et al., J. Difference Equ. Appl. 8, No. 2, 125--151 (2002; Zbl 0997.39007) Full Text: DOI
Marcellán, Francisco; Szafraniec, Franciszek Hugon The Sobolev-type moment problem. (English) Zbl 0951.44002 Proc. Am. Math. Soc. 128, No. 8, 2309-2317 (2000). Reviewer: Semyon Yakubovich (Porto) MSC: 44A60 46E39 47B37 47B65 PDF BibTeX XML Cite \textit{F. Marcellán} and \textit{F. H. Szafraniec}, Proc. Am. Math. Soc. 128, No. 8, 2309--2317 (2000; Zbl 0951.44002) Full Text: DOI
Álvarez de Morales, María; Pérez, Teresa E.; Piñar, Miguel A.; Ronveaux, André Non-standard orthogonality for Meixner polynomials. (English) Zbl 0949.33004 ETNA, Electron. Trans. Numer. Anal. 9, 1-25 (1999). Reviewer: W.Van Assche (Heverlee) MSC: 33C45 42C05 PDF BibTeX XML Cite \textit{M. Álvarez de Morales} et al., ETNA, Electron. Trans. Numer. Anal. 9, 1--25 (1999; Zbl 0949.33004) Full Text: EMIS EuDML
Foulquié Moreno, A.; Marcellán, F.; Peherstorfer, F.; Steinbauer, R. Strong asymptotics on the support of the measure of orthogonality for polynomials orthogonal with respect to a discrete Sobolev inner product on the unit circle. (English) Zbl 0907.42017 Proceedings of the 3rd international conference on functional analysis and approximation theory, Acquafredda di Maratea (Potenza), Italy, September 23–28, 1996. Vols. I and II. Palermo: Circolo Matemàtico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 52, 411-425 (1998). Reviewer: M.G.de Bruin (Delft) MSC: 42C05 PDF BibTeX XML Cite \textit{A. Foulquié Moreno} et al., in: Proceedings of the 3rd international conference on functional analysis and approximation theory, Acquafredda di Maratea (Potenza), Italy, September 23--28, 1996. Vols. I and II. Palermo: Circolo Matemàtico di Palermo. 411--425 (1998; Zbl 0907.42017)
Han, S. S.; Kwon, K. H.; Littlejohn, L. L. Zeros of orthogonal polynomials in certain discrete Sobolev spaces. (English) Zbl 0852.42014 J. Comput. Appl. Math. 67, No. 2, 309-325 (1996). MSC: 42C05 46E35 PDF BibTeX XML Cite \textit{S. S. Han} et al., J. Comput. Appl. Math. 67, No. 2, 309--325 (1996; Zbl 0852.42014) Full Text: DOI
López, G.; Marcellán, F.; Van Assche, Walter Relative asymptotics for polynomials orthogonal with respect to a discrete Sobolev inner product. (English) Zbl 0840.42017 Constructive Approximation 11, No. 1, 107-137 (1995). Reviewer: H.Stahl (Berlin) MSC: 42C05 PDF BibTeX XML Cite \textit{G. López} et al., Constr. Approx. 11, No. 1, 107--137 (1995; Zbl 0840.42017) Full Text: DOI
Alfaro, M.; Marcellán, F.; Meijer, H. G.; Rezola, M. L. Symmetric orthogonal polynomials for Sobolev-type inner products. (English) Zbl 0809.42012 J. Math. Anal. Appl. 184, No. 2, 360-381 (1994). Reviewer: W.Van Assche (Heverlee) MSC: 42C05 33C45 46E39 PDF BibTeX XML Cite \textit{M. Alfaro} et al., J. Math. Anal. Appl. 184, No. 2, 360--381 (1994; Zbl 0809.42012) Full Text: DOI
Meijer, H. G. On real and complex zeros of orthogonal polynomials in a discrete Sobolev space. (English) Zbl 0792.42011 J. Comput. Appl. Math. 49, No. 1-3, 179-191 (1993). MSC: 42C05 PDF BibTeX XML Cite \textit{H. G. Meijer}, J. Comput. Appl. Math. 49, No. 1--3, 179--191 (1993; Zbl 0792.42011) Full Text: DOI
Meijer, H. G. Laguerre polynomials generalized to a certain discrete Sobolev inner product space. (English) Zbl 0771.42015 J. Approximation Theory 73, No. 1, 1-16 (1993). MSC: 42C05 33C45 PDF BibTeX XML Cite \textit{H. G. Meijer}, J. Approx. Theory 73, No. 1, 1--16 (1993; Zbl 0771.42015) Full Text: DOI
Walter, Gilbert G. Discrete discrete wavelets. (English) Zbl 0752.42018 SIAM J. Math. Anal. 23, No. 4, 1004-1014 (1992). MSC: 42C40 42C10 46F10 PDF BibTeX XML Cite \textit{G. G. Walter}, SIAM J. Math. Anal. 23, No. 4, 1004--1014 (1992; Zbl 0752.42018) Full Text: DOI
Kornhuber, R. Local change of coordinates for grid-functions on regions with curved boundary. (English) Zbl 0681.65032 Math. Nachr. 139, 45-61 (1988). Reviewer: G.Stoyan MSC: 65J10 46E35 47A50 65N50 PDF BibTeX XML Cite \textit{R. Kornhuber}, Math. Nachr. 139, 45--61 (1988; Zbl 0681.65032) Full Text: DOI
Duran, Ricardo G. On polynomial approximation in Sobolev spaces. (English) Zbl 0523.41020 SIAM J. Numer. Anal. 20, 985-988 (1983). MSC: 41A65 41A10 46E39 PDF BibTeX XML Cite \textit{R. G. Duran}, SIAM J. Numer. Anal. 20, 985--988 (1983; Zbl 0523.41020) Full Text: DOI
Kroo, A. V. The correctness problem for best approximations by trigonometric polynomials in the class \(W^r_0H[\omega ]_c\). (English) Zbl 0419.42002 Math. Notes 22, 536-546 (1978). MSC: 42A10 41A10 41A50 46E39 PDF BibTeX XML Cite \textit{A. V. Kroo}, Math. Notes 22, 536--546 (1978; Zbl 0419.42002) Full Text: DOI