Fasondini, Marco; Olver, Sheehan; Xu, Yuan Orthogonal polynomials on a class of planar algebraic curves. (English) Zbl 07778802 Stud. Appl. Math. 151, No. 1, 369-405 (2023). Reviewer: Steven B. Damelin (Ann Arbor) MSC: 65F20 42C05 42C10 PDFBibTeX XMLCite \textit{M. Fasondini} et al., Stud. Appl. Math. 151, No. 1, 369--405 (2023; Zbl 07778802) Full Text: DOI arXiv OA License
Xu, Yuan Fourier orthogonal series on a paraboloid. (English) Zbl 1522.42059 J. Anal. Math. 149, No. 1, 251-279 (2023). Reviewer: Peter Massopust (München) MSC: 42C10 42C05 41A30 33C45 PDFBibTeX XMLCite \textit{Y. Xu}, J. Anal. Math. 149, No. 1, 251--279 (2023; Zbl 1522.42059) Full Text: DOI arXiv
Xu, Yuan Approximation and localized polynomial frame on double hyperbolic and conic domains. (English) Zbl 1528.41018 Constr. Approx. 57, No. 2, 921-976 (2023). MSC: 41A10 41A63 42C10 42C40 PDFBibTeX XMLCite \textit{Y. Xu}, Constr. Approx. 57, No. 2, 921--976 (2023; Zbl 1528.41018) Full Text: DOI arXiv
Xu, Yuan Bernstein inequality on conic domains and triangles. (English) Zbl 1525.41006 J. Approx. Theory 290, Article ID 105889, 30 p. (2023). MSC: 41A17 41A63 42C10 42C40 PDFBibTeX XMLCite \textit{Y. Xu}, J. Approx. Theory 290, Article ID 105889, 30 p. (2023; Zbl 1525.41006) Full Text: DOI arXiv
Aktaş, Rabia; Branquinho, Amílcar; Foulquié-Moreno, Ana; Xu, Yuan Monomial and Rodrigues orthogonal polynomials on the cone. (English) Zbl 07659446 J. Math. Anal. Appl. 522, No. 2, Article ID 126977, 26 p. (2023). Reviewer: Francisco Marcellán (Leganes) MSC: 33C45 42C05 41A10 42C15 PDFBibTeX XMLCite \textit{R. Aktaş} et al., J. Math. Anal. Appl. 522, No. 2, Article ID 126977, 26 p. (2023; Zbl 07659446) Full Text: DOI arXiv
Fasondini, Marco; Olver, Sheehan; Xu, Yuan Orthogonal polynomials on planar cubic curves. (English) Zbl 1523.33005 Found. Comput. Math. 23, No. 1, 1-31 (2023). Reviewer: Francisco Marcellán (Leganes) MSC: 33C50 42C05 42C10 65M70 PDFBibTeX XMLCite \textit{M. Fasondini} et al., Found. Comput. Math. 23, No. 1, 1--31 (2023; Zbl 1523.33005) Full Text: DOI arXiv
Xu, Yuan Orthogonal polynomials on domains of revolution. arXiv:2311.15554 Preprint, arXiv:2311.15554 [math.CA] (2023). MSC: 33C45 42C05 42C10 65D15 65D20 BibTeX Cite \textit{Y. Xu}, ``Orthogonal polynomials on domains of revolution'', Preprint, arXiv:2311.15554 [math.CA] (2023) Full Text: arXiv OA License
Ge, Yan; Xu, Yuan Sharp Bernstein inequalities on simplex. arXiv:2307.01839 Preprint, arXiv:2307.01839 [math.CA] (2023). MSC: 41A10 41A63 42C10 42C40 BibTeX Cite \textit{Y. Ge} and \textit{Y. Xu}, ``Sharp Bernstein inequalities on simplex'', Preprint, arXiv:2307.01839 [math.CA] (2023) Full Text: arXiv OA License
Sauer, Tomas; Xu, Yuan Continued fractions and orthogonal polynomials in several variables. arXiv:2303.16030 Preprint, arXiv:2303.16030 [math.CA] (2023). MSC: 41A21 42C05 65D15 65D32 BibTeX Cite \textit{T. Sauer} and \textit{Y. Xu}, ``Continued fractions and orthogonal polynomials in several variables'', Preprint, arXiv:2303.16030 [math.CA] (2023) Full Text: arXiv OA License
Xu, Yuan Maximal functions and multiplier theorem for Fourier orthogonal series. (English) Zbl 1516.41005 J. Funct. Anal. 283, No. 9, Article ID 109648, 33 p. (2022). MSC: 41A10 41A63 42B15 42C10 42C40 PDFBibTeX XMLCite \textit{Y. Xu}, J. Funct. Anal. 283, No. 9, Article ID 109648, 33 p. (2022; Zbl 1516.41005) Full Text: DOI arXiv
Iliev, Plamen; Xu, Yuan Hahn polynomials for hypergeometric distribution. (English) Zbl 1516.33009 Adv. Appl. Math. 139, Article ID 102364, 34 p. (2022). MSC: 33C50 33C70 42C05 PDFBibTeX XMLCite \textit{P. Iliev} and \textit{Y. Xu}, Adv. Appl. Math. 139, Article ID 102364, 34 p. (2022; Zbl 1516.33009) Full Text: DOI arXiv
Fernandez, Lidia; Perez, Teresa; Pinar, Miguel; Xu, Yuan Sobolev orthogonal polynomials on the conic surface. arXiv:2209.08186 Preprint, arXiv:2209.08186 [math.CA] (2022). MSC: 41A10 42C05 42C10 33C45 BibTeX Cite \textit{L. Fernandez} et al., ``Sobolev orthogonal polynomials on the conic surface'', Preprint, arXiv:2209.08186 [math.CA] (2022) Full Text: arXiv OA License
Xu, Yuan Approximation and localized polynomial frame on conic domains. (English) Zbl 1485.41006 J. Funct. Anal. 281, No. 12, Article ID 109257, 94 p. (2021). Reviewer: Francisco Pérez Acosta (La Laguna) MSC: 41A10 41A63 42C10 42C40 PDFBibTeX XMLCite \textit{Y. Xu}, J. Funct. Anal. 281, No. 12, Article ID 109257, 94 p. (2021; Zbl 1485.41006) Full Text: DOI arXiv
Olver, Sheehan; Xu, Yuan Non-homogeneous wave equation on a cone. (English) Zbl 1484.35141 Integral Transforms Spec. Funct. 32, No. 5-8, 604-619 (2021). MSC: 35C10 33C50 35L05 35L20 42C05 42C10 PDFBibTeX XMLCite \textit{S. Olver} and \textit{Y. Xu}, Integral Transforms Spec. Funct. 32, No. 5--8, 604--619 (2021; Zbl 1484.35141) Full Text: DOI arXiv
Xu, Yuan Laguerre expansions on conic domains. (English) Zbl 1485.33011 J. Fourier Anal. Appl. 27, No. 4, Paper No. 64, 36 p. (2021). Reviewer: D. L. Suthar (Dessie) MSC: 33C50 35C10 42C05 42C10 PDFBibTeX XMLCite \textit{Y. Xu}, J. Fourier Anal. Appl. 27, No. 4, Paper No. 64, 36 p. (2021; Zbl 1485.33011) Full Text: DOI arXiv
Xu, Yuan Orthogonal structure and orthogonal series in and on a double cone or a hyperboloid. (English) Zbl 1464.42017 Trans. Am. Math. Soc. 374, No. 5, 3603-3657 (2021). Reviewer: Pierluigi Vellucci (Roma) MSC: 42C05 42C10 33C50 35P10 PDFBibTeX XMLCite \textit{Y. Xu}, Trans. Am. Math. Soc. 374, No. 5, 3603--3657 (2021; Zbl 1464.42017) Full Text: DOI arXiv
Olver, Sheehan; Xu, Yuan Orthogonal structure on a quadratic curve. (English) Zbl 1460.33015 IMA J. Numer. Anal. 41, No. 1, 206-246 (2021). MSC: 33C47 PDFBibTeX XMLCite \textit{S. Olver} and \textit{Y. Xu}, IMA J. Numer. Anal. 41, No. 1, 206--246 (2021; Zbl 1460.33015) Full Text: DOI arXiv
Xu, Yuan Orthogonal polynomials and Fourier orthogonal series on a cone. (English) Zbl 07660967 J. Fourier Anal. Appl. 26, No. 3, Paper No. 36, 42 p. (2020). MSC: 42C10 42C05 33C45 35P10 41A10 41A63 PDFBibTeX XMLCite \textit{Y. Xu}, J. Fourier Anal. Appl. 26, No. 3, Paper No. 36, 42 p. (2020; Zbl 07660967) Full Text: DOI arXiv
Xu, Yuan Intertwining operators associated with dihedral groups. (English) Zbl 1455.33008 Constr. Approx. 52, No. 3, 395-422 (2020). Reviewer: Thomas Ernst (Uppsala) MSC: 33C80 33C45 33C50 44A20 PDFBibTeX XMLCite \textit{Y. Xu}, Constr. Approx. 52, No. 3, 395--422 (2020; Zbl 1455.33008) Full Text: DOI arXiv
Olver, Sheehan; Xu, Yuan Orthogonal polynomials in and on a quadratic surface of revolution. (English) Zbl 1503.42024 Math. Comput. 89, No. 326, 2847-2865 (2020). MSC: 42C05 42C10 65D15 65D32 65T50 PDFBibTeX XMLCite \textit{S. Olver} and \textit{Y. Xu}, Math. Comput. 89, No. 326, 2847--2865 (2020; Zbl 1503.42024) Full Text: DOI arXiv
Iliev, Plamen; Xu, Yuan Hahn polynomials on polyhedra and quantum integrability. (English) Zbl 1448.33012 Adv. Math. 364, Article ID 107032, 37 p. (2020). Reviewer: Nicolae Cotfas (Bucureşti) MSC: 33C50 33C80 81R12 PDFBibTeX XMLCite \textit{P. Iliev} and \textit{Y. Xu}, Adv. Math. 364, Article ID 107032, 37 p. (2020; Zbl 1448.33012) Full Text: DOI arXiv
Kerkyacharian, Gerard; Petrushev, Pencho; Xu, Yuan Gaussian bounds for the weighted heat kernels on the interval, ball, and simplex. (English) Zbl 1447.35166 Constr. Approx. 51, No. 1, 73-122 (2020). MSC: 35K08 42C05 PDFBibTeX XMLCite \textit{G. Kerkyacharian} et al., Constr. Approx. 51, No. 1, 73--122 (2020; Zbl 1447.35166) Full Text: DOI arXiv
Olver, Sheehan; Xu, Yuan Orthogonal structure on a wedge and on the boundary of a square. (English) Zbl 1428.42049 Found. Comput. Math. 19, No. 3, 561-589 (2019). Reviewer: Teresa A. Mesquita (Vila Nova de Famalicão) MSC: 42C05 42C10 33C50 PDFBibTeX XMLCite \textit{S. Olver} and \textit{Y. Xu}, Found. Comput. Math. 19, No. 3, 561--589 (2019; Zbl 1428.42049) Full Text: DOI arXiv
Feng, Han; Krattenthaler, Christian; Xu, Yuan Best polynomial approximation on the triangle. (English) Zbl 1414.41018 J. Approx. Theory 241, 63-78 (2019). Reviewer: Alexey Alimov (Moskva) MSC: 41A50 33C50 42C10 PDFBibTeX XMLCite \textit{H. Feng} et al., J. Approx. Theory 241, 63--78 (2019; Zbl 1414.41018) Full Text: DOI arXiv
Xu, Yuan Optimal points for cubature rules and polynomial interpolation on a square. (English) Zbl 1405.65034 Dick, Josef (ed.) et al., Contemporary computational mathematics – a celebration of the 80th birthday of Ian Sloan. In 2 volumes. Cham: Springer (ISBN 978-3-319-72455-3/hbk; 978-3-319-72456-0/ebook). 1287-1305 (2018). MSC: 65D32 65D05 33C45 41A50 PDFBibTeX XMLCite \textit{Y. Xu}, in: Contemporary computational mathematics -- a celebration of the 80th birthday of Ian Sloan. In 2 volumes. Cham: Springer. 1287--1305 (2018; Zbl 1405.65034) Full Text: DOI arXiv
Xu, Yuan Approximation by polynomials in Sobolev spaces with Jacobi weight. (English) Zbl 1405.41005 J. Fourier Anal. Appl. 24, No. 6, 1438-1459 (2018). Reviewer: Rostom Getsadze (Uppsala) MSC: 41A10 41A25 42C05 42C10 33C45 PDFBibTeX XMLCite \textit{Y. Xu}, J. Fourier Anal. Appl. 24, No. 6, 1438--1459 (2018; Zbl 1405.41005) Full Text: DOI arXiv
Piñar, Miguel A.; Xu, Yuan Best polynomial approximation on the unit ball. (English) Zbl 1480.41002 IMA J. Numer. Anal. 38, No. 3, 1209-1228 (2018). MSC: 41A10 41A50 PDFBibTeX XMLCite \textit{M. A. Piñar} and \textit{Y. Xu}, IMA J. Numer. Anal. 38, No. 3, 1209--1228 (2018; Zbl 1480.41002) Full Text: DOI arXiv
Xu, Yuan Positive definite functions on the unit sphere and integrals of Jacobi polynomials. (English) Zbl 1391.33026 Proc. Am. Math. Soc. 146, No. 5, 2039-2048 (2018). Reviewer: M. Abdessadek Saib (Tebessa) MSC: 33C45 33C50 42A82 60E10 PDFBibTeX XMLCite \textit{Y. Xu}, Proc. Am. Math. Soc. 146, No. 5, 2039--2048 (2018; Zbl 1391.33026) Full Text: DOI arXiv
Xu, Yuan Approximation and orthogonality in Sobolev spaces on a triangle. (English) Zbl 1377.41022 Constr. Approx. 46, No. 2, 349-434 (2017). Reviewer: Peter Massopust (München) MSC: 41A63 33C50 41A10 42C05 42C10 65M70 65N35 PDFBibTeX XMLCite \textit{Y. Xu}, Constr. Approx. 46, No. 2, 349--434 (2017; Zbl 1377.41022) Full Text: DOI arXiv
Iliev, Plamen; Xu, Yuan Connection coefficients for classical orthogonal polynomials of several variables. (English) Zbl 1365.33012 Adv. Math. 310, 290-326 (2017). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 33C50 33C70 42C05 PDFBibTeX XMLCite \textit{P. Iliev} and \textit{Y. Xu}, Adv. Math. 310, 290--326 (2017; Zbl 1365.33012) Full Text: DOI arXiv
Xu, Yuan Orthogonal expansions for generalized Gegenbauer weight function on the unit ball. (English) Zbl 1350.33018 Hardin, Douglas P. (ed.) et al., Modern trends in constructive function theory. Constructive functions 2014 conference in honor of Ed Saff’s 70th birthday, Vanderbilt University, Nashville, TN, USA, May 26–30, 2014. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2534-0/pbk; 978-1-4704-2934-8/ebook). Contemporary Mathematics 661, 153-165 (2016). MSC: 33C45 33C50 42C10 PDFBibTeX XMLCite \textit{Y. Xu}, Contemp. Math. 661, 153--165 (2016; Zbl 1350.33018) Full Text: DOI arXiv
Dimitrov, Dimitar K.; Xu, Yuan Slater determinants of orthogonal polynomials. (English) Zbl 1333.81449 J. Math. Anal. Appl. 435, No. 2, 1552-1572 (2016). MSC: 81V70 82B10 33C45 PDFBibTeX XMLCite \textit{D. K. Dimitrov} and \textit{Y. Xu}, J. Math. Anal. Appl. 435, No. 2, 1552--1572 (2016; Zbl 1333.81449) Full Text: DOI arXiv
Xu, Yuan An integral identity with applications in orthogonal polynomials. (English) Zbl 1331.33027 Proc. Am. Math. Soc. 143, No. 12, 5253-5263 (2015). Reviewer: Chrysoula G. Kokologiannaki (Patras) MSC: 33C45 33C50 42C10 PDFBibTeX XMLCite \textit{Y. Xu}, Proc. Am. Math. Soc. 143, No. 12, 5253--5263 (2015; Zbl 1331.33027) Full Text: DOI arXiv
Marcellán, Francisco; Xu, Yuan On Sobolev orthogonal polynomials. (English) Zbl 1351.33011 Expo. Math. 33, No. 3, 308-352 (2015). Reviewer: Jiří Hrivnák (Praha) MSC: 33C45 33C50 41A10 42C05 42C10 26C10 PDFBibTeX XMLCite \textit{F. Marcellán} and \textit{Y. Xu}, Expo. Math. 33, No. 3, 308--352 (2015; Zbl 1351.33011) Full Text: DOI arXiv
Xu, Yuan Generalized characteristic polynomials and Gaussian cubature rules. (English) Zbl 1320.33020 SIAM J. Matrix Anal. Appl. 36, No. 3, 1129-1142 (2015). MSC: 33C45 33C50 42C10 PDFBibTeX XMLCite \textit{Y. Xu}, SIAM J. Matrix Anal. Appl. 36, No. 3, 1129--1142 (2015; Zbl 1320.33020) Full Text: DOI arXiv
Dai, Feng; Xu, Yuan Erratum to: “The Hardy-Rellich inequality and uncertainty principle on the sphere”. (English) Zbl 1351.46029 Constr. Approx. 42, No. 1, 181-182 (2015). MSC: 46E35 26D10 42B10 42C10 33C45 33C55 PDFBibTeX XMLCite \textit{F. Dai} and \textit{Y. Xu}, Constr. Approx. 42, No. 1, 181--182 (2015; Zbl 1351.46029) Full Text: DOI
Xu, Yuan Hahn, Jacobi, and Krawtchouk polynomials of several variables. (English) Zbl 1317.33012 J. Approx. Theory 195, 19-42 (2015). Reviewer: P. K. Banerji (Jodhpur) MSC: 33C50 33C45 PDFBibTeX XMLCite \textit{Y. Xu}, J. Approx. Theory 195, 19--42 (2015; Zbl 1317.33012) Full Text: DOI arXiv
Fernández, Lidia; Marcellán, Francisco; Pérez, Teresa E.; Piñar, Miguel A.; Xu, Yuan Sobolev orthogonal polynomials on product domains. (English) Zbl 1312.33039 J. Comput. Appl. Math. 284, 202-215 (2015). MSC: 33C50 42C10 PDFBibTeX XMLCite \textit{L. Fernández} et al., J. Comput. Appl. Math. 284, 202--215 (2015; Zbl 1312.33039) Full Text: DOI arXiv
Xu, Yuan Uncertainty principle on weighted spheres, balls and simplexes. (English) Zbl 1312.42016 J. Approx. Theory 192, 193-214 (2015). Reviewer: Wen Yuan (Beijing) MSC: 42B10 42C10 PDFBibTeX XMLCite \textit{Y. Xu}, J. Approx. Theory 192, 193--214 (2015; Zbl 1312.42016) Full Text: DOI arXiv
Xu, Yuan Complex versus real orthogonal polynomials of two variables. (English) Zbl 1312.33035 Integral Transforms Spec. Funct. 26, No. 2, 134-151 (2015). Reviewer: Valery V. Karachik (Chelyabinsk) MSC: 33C45 33C50 33D45 PDFBibTeX XMLCite \textit{Y. Xu}, Integral Transforms Spec. Funct. 26, No. 2, 134--151 (2015; Zbl 1312.33035) Full Text: DOI arXiv
Dai, Feng; Xu, Yuan Tikhonov, Sergey (ed.) Analysis on \(h\)-harmonics and Dunkl transforms. Edited by Sergey Tikhonov. (English) Zbl 1323.33003 Advanced Courses in Mathematics – CRM Barcelona. Basel: Birkhäuser/Springer (ISBN 978-3-0348-0886-6/pbk; 978-3-0348-0887-3/ebook). viii, 118 p. (2015). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 33-02 33C50 33C55 41A10 42B10 42B25 PDFBibTeX XMLCite \textit{F. Dai} et al., Analysis on \(h\)-harmonics and Dunkl transforms. Edited by Sergey Tikhonov. Basel: Birkhäuser/Springer (2015; Zbl 1323.33003) Full Text: DOI
Dunkl, Charles F.; Xu, Yuan Orthogonal polynomials of several variables. 2nd ed. (English) Zbl 1317.33001 Encyclopedia of Mathematics and Its Applications 155. Cambridge: Cambridge University Press (ISBN 978-1-107-07189-6/hbk; 978-1-107-78613-4/ebook). xvii, 420 p. (2014). Reviewer: Bujar Fejzullahu (Presevo) MSC: 33-02 33C50 33C45 20F55 PDFBibTeX XMLCite \textit{C. F. Dunkl} and \textit{Y. Xu}, Orthogonal polynomials of several variables. 2nd ed. Cambridge: Cambridge University Press (2014; Zbl 1317.33001) Full Text: DOI
Dai, Feng; Xu, Yuan The Hardy-Rellich inequality and uncertainty principle on the sphere. (English) Zbl 1319.46026 Constr. Approx. 40, No. 1, 141-171 (2014); erratum ibid. 42, No. 2, 181-182 (2015). Reviewer: Sergey S. Volosivets (Saratov) MSC: 46E35 26D10 42B10 42C10 33C45 33C55 PDFBibTeX XMLCite \textit{F. Dai} and \textit{Y. Xu}, Constr. Approx. 40, No. 1, 141--171 (2014; Zbl 1319.46026) Full Text: DOI arXiv
Xu, Yuan Tight frame with Hahn and Krawtchouk polynomials of several variables. (English) Zbl 1293.33015 SIGMA, Symmetry Integrability Geom. Methods Appl. 10, Paper 019, 19 p. (2014). MSC: 33C50 42C15 PDFBibTeX XMLCite \textit{Y. Xu}, SIGMA, Symmetry Integrability Geom. Methods Appl. 10, Paper 019, 19 p. (2014; Zbl 1293.33015) Full Text: DOI arXiv EMIS
Aktaş, Rabia; Xu, Yuan Sobolev orthogonal polynomials on a simplex. (English) Zbl 1316.33006 Int. Math. Res. Not. 2013, No. 13, 3087-3131 (2013). MSC: 33C50 42C05 PDFBibTeX XMLCite \textit{R. Aktaş} and \textit{Y. Xu}, Int. Math. Res. Not. 2013, No. 13, 3087--3131 (2013; Zbl 1316.33006) Full Text: DOI arXiv
Pérez, Teresa E.; Piñar, Miguel A.; Xu, Yuan Weighted Sobolev orthogonal polynomials on the unit ball. (English) Zbl 1281.42026 J. Approx. Theory 171, 84-104 (2013). MSC: 42C05 PDFBibTeX XMLCite \textit{T. E. Pérez} et al., J. Approx. Theory 171, 84--104 (2013; Zbl 1281.42026) Full Text: DOI arXiv
Dai, Feng; Xu, Yuan Approximation theory and harmonic analysis on spheres and balls. (English) Zbl 1275.42001 Springer Monographs in Mathematics. New York, NY: Springer (ISBN 978-1-4614-6659-8/hbk; 978-1-4614-6660-4/ebook). xviii, 440 p. (2013). Reviewer: Elijah Liflyand (Ramat-Gan) MSC: 42-02 41-02 42A10 42C10 43A90 PDFBibTeX XMLCite \textit{F. Dai} and \textit{Y. Xu}, Approximation theory and harmonic analysis on spheres and balls. New York, NY: Springer (2013; Zbl 1275.42001) Full Text: DOI
Dai, F.; Xu, Y. Spherical Harmonics. arXiv:1304.2585 Preprint, arXiv:1304.2585 [math.CA] (2013). MSC: 42B10 42C10 BibTeX Cite \textit{F. Dai} and \textit{Y. Xu}, ``Spherical Harmonics'', Preprint, arXiv:1304.2585 [math.CA] (2013) Full Text: arXiv OA License
Li, Huiyuan; Sun, Jiachang; Xu, Yuan Discrete Fourier analysis and Chebyshev polynomials with \(G_{2}\) group. (English) Zbl 1270.41002 SIGMA, Symmetry Integrability Geom. Methods Appl. 8, Paper 067, 29 p. (2012). MSC: 41A05 41A10 PDFBibTeX XMLCite \textit{H. Li} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 8, Paper 067, 29 p. (2012; Zbl 1270.41002) Full Text: DOI arXiv
Xu, Yuan Orthogonal polynomials and expansions for a family of weight functions in two variables. (English) Zbl 1264.33017 Constr. Approx. 36, No. 2, 161-190 (2012). Reviewer: Joseph Lakey (Las Cruces) MSC: 33C50 42C10 PDFBibTeX XMLCite \textit{Y. Xu}, Constr. Approx. 36, No. 2, 161--190 (2012; Zbl 1264.33017) Full Text: DOI arXiv
Delgado, Antonia M.; Fernández, Lidia; Pérez, Teresa E.; Piñar, Miguel A.; Xu, Yuan Orthogonal polynomials in several variables for measures with mass points. (English) Zbl 1205.33020 Numer. Algorithms 55, No. 2-3, 245-264 (2010). Reviewer: Nele De Schepper (Gent) MSC: 33C50 42C05 PDFBibTeX XMLCite \textit{A. M. Delgado} et al., Numer. Algorithms 55, No. 2--3, 245--264 (2010; Zbl 1205.33020) Full Text: DOI arXiv
Ivanov, Kamen; Petrushev, Pencho; Xu, Yuan Sub-exponentially localized kernels and frames induced by orthogonal expansions. (English) Zbl 1194.42035 Math. Z. 264, No. 2, 361-397 (2010). Reviewer: Vladimir V. Kisil (Leeds) MSC: 42C10 42C40 33C99 PDFBibTeX XMLCite \textit{K. Ivanov} et al., Math. Z. 264, No. 2, 361--397 (2010; Zbl 1194.42035) Full Text: DOI arXiv
Fernández, Lidia; Pérez, Teresa E.; Piñar, Miguel A.; Xu, Yuan Krall-type orthogonal polynomials in several variables. (English) Zbl 1183.33020 J. Comput. Appl. Math. 233, No. 6, 1519-1524 (2010). Reviewer: Chrysoula G. Kokologiannaki (Patras) MSC: 33C50 42C05 PDFBibTeX XMLCite \textit{L. Fernández} et al., J. Comput. Appl. Math. 233, No. 6, 1519--1524 (2010; Zbl 1183.33020) Full Text: DOI arXiv
Castell, W. Zu; Filbir, F.; Xu, Y. Cesàro means of Jacobi expansions on the parabolic biangle. (English) Zbl 1184.26027 J. Approx. Theory 159, No. 2, 167-179 (2009). Reviewer: József Sándor (Cluj-Napoca) MSC: 26E60 41A58 42A38 PDFBibTeX XMLCite \textit{W. Z. Castell} et al., J. Approx. Theory 159, No. 2, 167--179 (2009; Zbl 1184.26027) Full Text: DOI arXiv
Dai, Feng; Xu, Yuan Cesàro means of orthogonal expansions in several variables. (English) Zbl 1173.42310 Constr. Approx. 29, No. 1, 129-155 (2009). MSC: 42B08 33C50 42C10 PDFBibTeX XMLCite \textit{F. Dai} and \textit{Y. Xu}, Constr. Approx. 29, No. 1, 129--155 (2009; Zbl 1173.42310) Full Text: DOI arXiv
Piñar, Miguel; Xu, Yuan Orthogonal polynomials and partial differential equations on the unit ball. (English) Zbl 1178.33009 Proc. Am. Math. Soc. 137, No. 9, 2979-2987 (2009). Reviewer: Wolfram Koepf (Kassel) MSC: 33C50 33E30 PDFBibTeX XMLCite \textit{M. Piñar} and \textit{Y. Xu}, Proc. Am. Math. Soc. 137, No. 9, 2979--2987 (2009; Zbl 1178.33009) Full Text: DOI arXiv
Delgado, Antonia M.; Geronimo, Jeffrey S.; Iliev, Plamen; Xu, Yuan On a two-variable class of Bernstein-Szegő measures. (English) Zbl 1171.42306 Constr. Approx. 30, No. 1, 71-91 (2009). MSC: 42C05 30E05 47A57 PDFBibTeX XMLCite \textit{A. M. Delgado} et al., Constr. Approx. 30, No. 1, 71--91 (2009; Zbl 1171.42306) Full Text: DOI arXiv
Dai, Feng; Xu, Yuan Boundedness of projection operators and Cesàro means in weighted \(L^p\) space on the unit sphere. (English) Zbl 1173.33011 Trans. Am. Math. Soc. 361, No. 6, 3189-3221 (2009). Reviewer: Ahmed I. Zayed (Chicago) MSC: 33C50 42B08 42C10 PDFBibTeX XMLCite \textit{F. Dai} and \textit{Y. Xu}, Trans. Am. Math. Soc. 361, No. 6, 3189--3221 (2009; Zbl 1173.33011) Full Text: DOI arXiv
Kerkyacharian, G.; Petrushev, P.; Picard, D.; Xu, Yuan Decomposition of Triebel-Lizorkin and Besov spaces in the context of Laguerre expansions. (English) Zbl 1163.42010 J. Funct. Anal. 256, No. 4, 1137-1188 (2009). Reviewer: Som Prakash Goyal (Jaipur) MSC: 42C05 46F99 PDFBibTeX XMLCite \textit{G. Kerkyacharian} et al., J. Funct. Anal. 256, No. 4, 1137--1188 (2009; Zbl 1163.42010) Full Text: DOI arXiv
Li, Huiyuan; Sun, Jiachang; Xu, Yuan Discrete Fourier analysis, cubature, and interpolation on a hexagon and a triangle. (English) Zbl 1179.41002 SIAM J. Numer. Anal. 46, No. 4, 1653-1681 (2008). Reviewer: Alexei Lukashov (Istanbul) MSC: 41A05 41A63 42B05 41A55 65D32 PDFBibTeX XMLCite \textit{H. Li} et al., SIAM J. Numer. Anal. 46, No. 4, 1653--1681 (2008; Zbl 1179.41002) Full Text: DOI arXiv
Xu, Yuan Sobolev orthogonal polynomials defined via gradient on the unit ball. (English) Zbl 1197.42016 J. Approx. Theory 152, No. 1, 52-65 (2008). MSC: 42C10 33C55 PDFBibTeX XMLCite \textit{Y. Xu}, J. Approx. Theory 152, No. 1, 52--65 (2008; Zbl 1197.42016) Full Text: DOI arXiv
Xu, Yuan Reconstruction from Radon projections and orthogonal expansion on a ball. (English) Zbl 1125.33009 J. Phys. A, Math. Theor. 40, No. 26, 7239-7253 (2007). Reviewer: Alexei Lukashov (Istanbul) MSC: 33C50 44A12 42C05 PDFBibTeX XMLCite \textit{Y. Xu}, J. Phys. A, Math. Theor. 40, No. 26, 7239--7253 (2007; Zbl 1125.33009) Full Text: DOI arXiv
Iliev, Plamen; Xu, Yuan Discrete orthogonal polynomials and difference equations of several variables. (English) Zbl 1133.47027 Adv. Math. 212, No. 1, 1-36 (2007). Reviewer: Bilender P. Allahverdiev (Isparta) MSC: 47B39 42C05 39A12 39A20 33C45 PDFBibTeX XMLCite \textit{P. Iliev} and \textit{Y. Xu}, Adv. Math. 212, No. 1, 1--36 (2007; Zbl 1133.47027) Full Text: DOI arXiv
Baratchart, L.; Martínez-Finkelshtein, A.; Jimenez, D.; Lubinsky, D. S.; Mhaskar, H. N.; Pritsker, I.; Putinar, M.; Stylianopoulos, N.; Totik, V.; Varju, P.; Xu, Y. Open problems in constructive function theory. (English) Zbl 1107.41011 ETNA, Electron. Trans. Numer. Anal. 25, 511-525 (2006). MSC: 41A17 41A21 41A55 41A99 42C15 PDFBibTeX XMLCite \textit{L. Baratchart} et al., ETNA, Electron. Trans. Numer. Anal. 25, 511--525 (2006; Zbl 1107.41011) Full Text: EuDML Link
Xu, Yuan Analysis on the unit ball and on the simplex. (English) Zbl 1107.41008 ETNA, Electron. Trans. Numer. Anal. 25, 284-301 (2006). MSC: 41A10 42C10 41A63 PDFBibTeX XMLCite \textit{Y. Xu}, ETNA, Electron. Trans. Numer. Anal. 25, 284--301 (2006; Zbl 1107.41008) Full Text: EuDML Link
Xu, Yuan A family of Sobolev orthogonal polynomials on the unit ball. (English) Zbl 1092.42016 J. Approximation Theory 138, No. 2, 232-241 (2006). Reviewer: Alexei Lukashov (Saratov) MSC: 42C05 33C50 PDFBibTeX XMLCite \textit{Y. Xu}, J. Approx. Theory 138, No. 2, 232--241 (2006; Zbl 1092.42016) Full Text: DOI arXiv
Xu, Yuan Lecture notes on orthogonal polynomials of several variables. (English) Zbl 1145.42007 zu Castell, Wolfgang (ed.) et al., Inzell lectures on orthogonal polynomials. Lectures from the 2nd summer school, Inzell, Germany, September 17–21, 2001. Hauppauge, NY: Nova Science Publishers (ISBN 1-59454-108-6/hbk). Advances in the Theory of Special Functions and Orthogonal Polynomials, 141-196 (2005). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 42C05 33-02 33C45 42C10 PDFBibTeX XMLCite \textit{Y. Xu}, in: Inzell lectures on orthogonal polynomials. Lectures from the 2nd summer school, Inzell, Germany, September 17--21, 2001. Hauppauge, NY: Nova Science Publishers. 141--196 (2005; Zbl 1145.42007)
Vértesi, P.; Xu, Y. Mean convergence of orthogonal Fourier series and interpolating polynomials. (English) Zbl 1094.42028 Acta Math. Hung. 107, No. 1-2, 119-147 (2005). Reviewer: Wolfram Koepf (Kassel) MSC: 42C10 33C50 PDFBibTeX XMLCite \textit{P. Vértesi} and \textit{Y. Xu}, Acta Math. Hung. 107, No. 1--2, 119--147 (2005; Zbl 1094.42028) Full Text: DOI arXiv
Xu, Yuan Almost everywhere convergence of orthogonal expansions of several variables. (English) Zbl 1084.33010 Constructive Approximation 22, No. 1, 67-93 (2005). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 33C50 42C05 41A60 42B25 PDFBibTeX XMLCite \textit{Y. Xu}, Constr. Approx. 22, No. 1, 67--93 (2005; Zbl 1084.33010) Full Text: DOI arXiv
Xu, Yuan Monomial orthogonal polynomials of several variables. (English) Zbl 1081.33020 J. Approximation Theory 133, No. 1, 1-37 (2005). Reviewer: Margit Roesler (Darmstadt) MSC: 33C52 33C50 42C15 PDFBibTeX XMLCite \textit{Y. Xu}, J. Approx. Theory 133, No. 1, 1--37 (2005; Zbl 1081.33020) Full Text: DOI
Xu, Yuan Second-order difference equations and discrete orthogonal polynomials of two variables. (English) Zbl 1074.39001 Int. Math. Res. Not. 2005, No. 8, 451-475 (2005). Reviewer: Alexei Yu. Karlovich (Braga) MSC: 39A10 42C05 PDFBibTeX XMLCite \textit{Y. Xu}, Int. Math. Res. Not. 2005, No. 8, 451--475 (2005; Zbl 1074.39001) Full Text: DOI arXiv
Xu, Yuan Generalized translation operator and approximation in several variables. (English) Zbl 1083.42023 J. Comput. Appl. Math. 178, No. 1-2, 489-512 (2005). Reviewer: Mariano Gasca (Zaragoza) MSC: 42C15 33C50 41A30 41A63 PDFBibTeX XMLCite \textit{Y. Xu}, J. Comput. Appl. Math. 178, No. 1--2, 489--512 (2005; Zbl 1083.42023) Full Text: DOI arXiv
Xu, Yuan Weighted approximation of functions on the unit sphere. (English) Zbl 1069.33014 Constructive Approximation 21, No. 1, 1-28 (2005). Reviewer: Luigi Gatteschi (Torino) MSC: 33C50 42C10 PDFBibTeX XMLCite \textit{Y. Xu}, Constr. Approx. 21, No. 1, 1--28 (2005; Zbl 1069.33014) Full Text: DOI arXiv
Xu, Yuan Rodrigues type formula for orthogonal polynomials on the unit ball. (English) Zbl 1145.33303 Proc. Am. Math. Soc. 133, No. 7, 1965-1976 (2005). MSC: 33C50 42C05 PDFBibTeX XMLCite \textit{Y. Xu}, Proc. Am. Math. Soc. 133, No. 7, 1965--1976 (2005; Zbl 1145.33303) Full Text: DOI
Xu, Yuan On discrete orthogonal polynomials of several variables. (English) Zbl 1069.33011 Adv. Appl. Math. 33, No. 3, 615-632 (2004). Reviewer: Roelof Koekoek (Delft) MSC: 33C45 42C05 PDFBibTeX XMLCite \textit{Y. Xu}, Adv. Appl. Math. 33, No. 3, 615--632 (2004; Zbl 1069.33011) Full Text: DOI arXiv
Xu, Yuan Approximation by means of \(h\)-harmonic polynomials on the unit sphere. (English) Zbl 1043.42022 Adv. Comput. Math. 21, No. 1-2, 37-58 (2004). MSC: 42C15 33C50 PDFBibTeX XMLCite \textit{Y. Xu}, Adv. Comput. Math. 21, No. 1--2, 37--58 (2004; Zbl 1043.42022) Full Text: DOI
Xu, Yuan Orthogonal expansions and weighted approximation on the unit sphere. (English) Zbl 1036.41010 Bojanov, B. D., Constructive theory of functions. Proceedings of the international conference, Varna, Bulgaria, June 19–23, 2002. Sofia: DARBA (ISBN 954-90126-6-2/hbk). 156-177 (2003). Reviewer: Aleksey A. Dovgoshey (Donetsk) MSC: 41A25 41A10 42C15 33C52 PDFBibTeX XMLCite \textit{Y. Xu}, in: Constructive theory of functions. Proceedings of the international conference, Varna, Bulgaria, June 19--23, 2002. Sofia: DARBA. 156--177 (2003; Zbl 1036.41010)
Xu, Yuan Biorthogonal polynomials and total positive functions. (English) Zbl 1041.42020 J. Phys. A, Math. Gen. 35, No. 26, 5499-5510 (2002). MSC: 42C05 33C45 PDFBibTeX XMLCite \textit{Y. Xu}, J. Phys. A, Math. Gen. 35, No. 26, 5499--5510 (2002; Zbl 1041.42020) Full Text: DOI
Xu, Yuan An integral formula for generalized Gegenbauer polynomials and Jacobi polynomials. (English) Zbl 1013.33006 Adv. Appl. Math. 29, No. 2, 328-343 (2002). Reviewer: P.K.Mital (Ajmer) MSC: 33C45 33C47 PDFBibTeX XMLCite \textit{Y. Xu}, Adv. Appl. Math. 29, No. 2, 328--343 (2002; Zbl 1013.33006) Full Text: DOI
Xu, Yuan Representation of reproducing kernels and the Lebesgue constants on the ball. (English) Zbl 0988.42016 J. Approximation Theory 112, No. 2, 295-310 (2001). MSC: 42C05 PDFBibTeX XMLCite \textit{Y. Xu}, J. Approx. Theory 112, No. 2, 295--310 (2001; Zbl 0988.42016) Full Text: DOI Link
Xu, Yuan Orthogonal polynomials on the ball and the simplex for weight functions with reflection symmetries. (English) Zbl 0985.33007 Constructive Approximation 17, No. 3, 383-412 (2001). Reviewer: Som Prakash Goyal (Jaipur) MSC: 33C52 33C45 33C80 81R12 PDFBibTeX XMLCite \textit{Y. Xu}, Constr. Approx. 17, No. 3, 383--412 (2001; Zbl 0985.33007) Full Text: DOI
Xu, Yuan Orthogonal polynomials and summability in Fourier orthogonal series on spheres and on balls. (English) Zbl 0992.42007 Math. Proc. Camb. Philos. Soc. 131, No. 1, 139-155 (2001). Reviewer: Ferenc Móricz (Szeged) MSC: 42C05 PDFBibTeX XMLCite \textit{Y. Xu}, Math. Proc. Camb. Philos. Soc. 131, No. 1, 139--155 (2001; Zbl 0992.42007) Full Text: DOI
Xu, Yuan Orthogonal polynomials and cubature formulae on balls, simplices, and spheres. (English) Zbl 0972.42016 J. Comput. Appl. Math. 127, No. 1-2, 349-368 (2001). Reviewer: Marcel G.de Bruin (Delft) MSC: 42C05 33C45 41A55 65D32 PDFBibTeX XMLCite \textit{Y. Xu}, J. Comput. Appl. Math. 127, No. 1--2, 349--368 (2001; Zbl 0972.42016) Full Text: DOI
Dunkl, Charles F.; Xu, Yuan Orthogonal polynomials of several variables. (English) Zbl 0964.33001 Encyclopedia of Mathematics and Its Applications. 81. Cambridge: Cambridge University Press. xv, 390 p. (2001). Reviewer: A.Klimyk (Kyïv) MSC: 33-02 33C50 PDFBibTeX XMLCite \textit{C. F. Dunkl} and \textit{Y. Xu}, Orthogonal polynomials of several variables. Cambridge: Cambridge University Press (2001; Zbl 0964.33001)
Xu, Yuan A product formula for Jacobi polynomials. (English) Zbl 1097.33508 Dunkl, Charles (ed.) et al., Special functions. Proceedings of the international workshop on special functions – asymptotics, harmonic analysis and mathematical physics, Hong Kong, China, June 21–25, 1999. Singapore: World Scientific (ISBN 981-02-4393-6/hbk). 423-430 (2000). MSC: 33C45 PDFBibTeX XMLCite \textit{Y. Xu}, in: Special functions. Proceedings of the international workshop on special functions -- asymptotics, harmonic analysis and mathematical physics, Hong Kong, China, June 21--25, 1999. Singapore: World Scientific. 423--430 (2000; Zbl 1097.33508) Full Text: DOI Link
Xu, Yuan Harmonic polynomials associated with reflection groups. (English) Zbl 0965.33006 Can. Math. Bull. 43, No. 4, 496-507 (2000). Reviewer: Michael Voit (Tübingen) MSC: 33C50 33C52 33C45 PDFBibTeX XMLCite \textit{Y. Xu}, Can. Math. Bull. 43, No. 4, 496--507 (2000; Zbl 0965.33006) Full Text: DOI
Xu, Yuan Funk-Hecke formula for orthogonal polynomials on spheres and on balls. (English) Zbl 1032.33005 Bull. Lond. Math. Soc. 32, No. 4, 447-457 (2000). MSC: 33C55 42C05 PDFBibTeX XMLCite \textit{Y. Xu}, Bull. Lond. Math. Soc. 32, No. 4, 447--457 (2000; Zbl 1032.33005) Full Text: DOI
Xu, Yuan A note on summability of multiple Laguerre expansions. (English) Zbl 0959.42017 Proc. Am. Math. Soc. 128, No. 12, 3571-3578 (2000). Reviewer: Elijah Liflyand (Ramat-Gan) MSC: 42C10 26C05 41A63 33C50 42C20 41A58 PDFBibTeX XMLCite \textit{Y. Xu}, Proc. Am. Math. Soc. 128, No. 12, 3571--3578 (2000; Zbl 0959.42017) Full Text: DOI
Li, Zhongkai; Xu, Yuan Summability of product Jacobi expansions. (English) Zbl 0971.42022 J. Approximation Theory 104, No. 2, 287-301 (2000). Reviewer: Marcel G.de Bruin (Delft) MSC: 42C15 42C05 PDFBibTeX XMLCite \textit{Z. Li} and \textit{Y. Xu}, J. Approx. Theory 104, No. 2, 287--301 (2000; Zbl 0971.42022) Full Text: DOI
Xu, Yuan Constructing cubature formulae by the method of reproducing kernel. (English) Zbl 0947.41024 Numer. Math. 85, No. 1, 155-173 (2000). Reviewer: Váslaw Burjan (Praha) MSC: 41A55 33C50 42C05 41A63 PDFBibTeX XMLCite \textit{Y. Xu}, Numer. Math. 85, No. 1, 155--173 (2000; Zbl 0947.41024) Full Text: DOI
Xu, Yuan Polynomial interpolation in several variables, cubature formulae, and ideals. (English) Zbl 0943.41002 Adv. Comput. Math. 12, No. 4, 363-376 (2000). Reviewer: Luigi Gatteschi (Torino) MSC: 41A05 41A10 41A63 65D05 41A55 PDFBibTeX XMLCite \textit{Y. Xu}, Adv. Comput. Math. 12, No. 4, 363--376 (2000; Zbl 0943.41002) Full Text: DOI
Xu, Yuan Asymptotics of the Christoffel functions on a simplex in \(\mathbb{R}^d\). (English) Zbl 0943.42012 J. Approximation Theory 99, No. 1, 122-133 (1999). Reviewer: Marcel G.de Bruin (Delft) MSC: 42C05 33C45 PDFBibTeX XMLCite \textit{Y. Xu}, J. Approx. Theory 99, No. 1, 122--133 (1999; Zbl 0943.42012) Full Text: DOI
Xu, Yuan Summability of Fourier orthogonal series for Jacobi weight on a ball in \(\mathbb{R}^{d}\). (English) Zbl 0929.42016 Trans. Am. Math. Soc. 351, No. 6, 2439-2458 (1999). Reviewer: J.P.Singhal (Baroda) MSC: 42C05 33C50 42C15 PDFBibTeX XMLCite \textit{Y. Xu}, Trans. Am. Math. Soc. 351, No. 6, 2439--2458 (1999; Zbl 0929.42016) Full Text: DOI
Xu, Yuan Orthogonal polynomials and cubature formulae on spheres and on simplices. (English) Zbl 0913.33005 Methods Appl. Anal. 5, No. 2, 169-184 (1998). Reviewer: Luigi Gatteschi (Torino) MSC: 33C50 33C55 65D32 PDFBibTeX XMLCite \textit{Y. Xu}, Methods Appl. Anal. 5, No. 2, 169--184 (1998; Zbl 0913.33005) Full Text: DOI
Xu, Yuan Summability of Fourier orthogonal series for Jacobi weight functions on the simplex in \(\mathbb{R}^d\). (English) Zbl 0918.42015 Proc. Am. Math. Soc. 126, No. 10, 3027-3036 (1998). Reviewer: A.Martínez Finkelshtein (Almeria) MSC: 42C05 41A63 33C50 41A10 PDFBibTeX XMLCite \textit{Y. Xu}, Proc. Am. Math. Soc. 126, No. 10, 3027--3036 (1998; Zbl 0918.42015) Full Text: DOI
Xu, Yuan Intertwining operator and \(h\)-harmonics associated with reflection groups. (English) Zbl 0905.33005 Can. J. Math. 50, No. 1, 193-209 (1998). Reviewer: V.Burjan (Praha) MSC: 33C50 33C45 33C80 PDFBibTeX XMLCite \textit{Y. Xu}, Can. J. Math. 50, No. 1, 193--209 (1998; Zbl 0905.33005) Full Text: DOI
Xu, Yuan Orthogonal polynomials and cubature formulae on spheres and on balls. (English) Zbl 0907.33005 SIAM J. Math. Anal. 29, No. 3, 779-793 (1998). MSC: 33C50 33C55 65D32 PDFBibTeX XMLCite \textit{Y. Xu}, SIAM J. Math. Anal. 29, No. 3, 779--793 (1998; Zbl 0907.33005) Full Text: DOI
Xu, Yuan Summability of certain product ultraspherical orthogonal series in several variables. (English) Zbl 0884.42019 Ann. Numer. Math. 4, No. 1-4, 623-638 (1997). Reviewer: M.G.de Bruin (Delft) MSC: 42C15 33C45 PDFBibTeX XMLCite \textit{Y. Xu}, Ann. Numer. Math. 4, No. 1--4, 623--638 (1997; Zbl 0884.42019)
Xu, Yuan Integration of the intertwining operator for \(h\)-harmonic polynomials associated to reflection groups. (English) Zbl 0881.33010 Proc. Am. Math. Soc. 125, No. 10, 2963-2973 (1997). MSC: 33C50 33C45 42C10 PDFBibTeX XMLCite \textit{Y. Xu}, Proc. Am. Math. Soc. 125, No. 10, 2963--2973 (1997; Zbl 0881.33010) Full Text: DOI
Xu, Yuan On orthogonal polynomials in several variables. (English) Zbl 0873.42016 Ismail, Mourad E. H. (ed.) et al., Special functions, \(q\)-series and related topics. Providence, RI: American Mathematical Society. Fields Inst. Commun. 14, 247-270 (1997). Reviewer: M.Reimer (Dortmund) MSC: 42C05 65D32 41A10 41A63 PDFBibTeX XMLCite \textit{Y. Xu}, Fields Inst. Commun. 14, 247--270 (1997; Zbl 0873.42016)