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Applicable Analysis
An International Journal
Volume 33, 1989 - Issue 1-2
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Original Articles

Orthogonal polynomials with respect to a symmetric inner product involving derivatives

H. Bavinck Department of Mathematics and Informatics, Delft University of Technology, Julianalaan, BL Delft, 132, 2628, The Netherlands
&
H.G. Meijer Department of Mathematics and Informatics, Delft University of Technology, Julianalaan, BL Delft, 132, 2628, The Netherlands
Pages 103-117 | Received 22 Nov 1988, Published online: 02 May 2007

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M. Alfaro, F. Marcellán & M.L. Rezola. (1997) Estimates for jacobi—sobolev type orthogonal polynomials. Applicable Analysis 67:1-2, pages 157-174.
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Articles from other publishers (29)

Sergey Zagorodnyuk. (2023) On some hypergeometric Sobolev orthogonal polynomials with several continuous parameters. V. N. Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics:98, pages 4-24.
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Boris Petrovich Osilenker. (2022) On multipliers for Fourier series in Sobolev orthogonal polynomials. Sbornik: Mathematics 213:8, pages 1058-1095.
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Boris Petrovich Osilenker. (2022) О мультипликаторах рядов Фурье по ортогональным многочленам СоболеваOn multipliers for Fourier series in Sobolev orthogonal polynomials. Математический сборник Matematicheskii Sbornik 213:8, pages 44-82.
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Juan C. García-Ardila, Francisco Marcellán & Misael E. Marriaga. 2020. Orthogonal Polynomials. Orthogonal Polynomials 245 292 .
Clemens Markett. (2015) New representation and factorizations of the higher-order ultraspherical-type differential equations. Journal of Mathematical Analysis and Applications 421:1, pages 244-259.
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Francisco Marcellán & Yuan Xu. (2015) On Sobolev orthogonal polynomials. Expositiones Mathematicae 33:3, pages 308-352.
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Bujar Xh. Fejzullahu & Francisco Marcellán. (2013) A Cohen type inequality for Gegenbauer-Sobolev expansions. Rocky Mountain Journal of Mathematics 43:1.
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Cleonice F. Bracciali, Laura Castaño-García & Juan J. Moreno-Balcázar. (2010) Some asymptotics for Sobolev orthogonal polynomials involving Gegenbauer weights. Journal of Computational and Applied Mathematics 235:4, pages 904-915.
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E. X. L. de Andrade, C. F. Bracciali & A. Sri Ranga. (2008) Zeros of Gegenbauer-Sobolev Orthogonal Polynomials: Beyond Coherent Pairs. Acta Applicandae Mathematicae 105:1, pages 65-82.
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Fejzullahu BujarX.X.. (2008) A Cohen type inequality for Legendre-Sobolev expansions. Filomat 22:1, pages 23-31.
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B. P. Osilenker. (2007) An extremal problem for algebraic polynomials in the symmetric discrete Gegenbauer-Sobolev space. Mathematical Notes 82:3-4, pages 366-379.
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Борис Петрович Осиленкер & Boris Petrovich Osilenker. (2007) Об одной экстремальной задаче для алгебраических полиномов в симметричном дискретном пространстве Гегенбауэра - СоболеваAn Extremal Problem for Algebraic Polynomials in the Symmetric Discrete Gegenbauer - Sobolev Space. Математические заметки Matematicheskie Zametki 82:3, pages 411-425.
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Diego Dominici. (2007) Some remarks on a paper by L. Carlitz. Journal of Computational and Applied Mathematics 198:1, pages 129-142.
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Boris P. Osilenker. (2006) Generalized trace formula and asymptotics of the averaged Turan determinant for polynomials orthogonal with a discrete Sobolev inner product. Journal of Approximation Theory 141:1, pages 70-97.
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H. Bavinck. 2003. Advanced Problems in Constructive Approximation. Advanced Problems in Constructive Approximation 1 20 .
Jorge Sánchez-Ruiz & Jesús S. Dehesa. (2001) Some connection and linearization problems for polynomials in and beyond the Askey scheme. Journal of Computational and Applied Mathematics 133:1-2, pages 579-591.
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H. Bavinck. (2000) Differential operators having Sobolev-type Gegenbauer polynomials as eigenfunctions. Journal of Computational and Applied Mathematics 118:1-2, pages 23-42.
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H. Bavinck & J. Koekoek. (1999) Differential operators having symmetric orthogonal polynomials as eigenfunctions. Journal of Computational and Applied Mathematics 106:2, pages 369-393.
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J. Arvesú, R. Álvarez-Nodarse, F. Marcellán & K. Pan. (1998) Jacobi-Sobolev-type orthogonal polynomials: Second-order differential equation and zeros. Journal of Computational and Applied Mathematics 90:2, pages 135-156.
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F. Marcellan & B. P. Osilenker. (1997) Estimates of polynomials orthogonal with respect to the Legendre-Sobolev inner product. Mathematical Notes 62:6, pages 731-738.
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Ф Марчелан, F Marcellan, Борис Петрович Осиленкер & Boris Petrovich Osilenker. (1997) Оценки полиномов, ортогональных по отношению к скалярному произведению Лежандра - СоболеваEstimates of polynomials orthogonal with respect to the Legendre - Sobolev inner product. Математические заметки Matematicheskie Zametki 62:6, pages 871-880.
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Teresa E. Pérez & Miguel A. Piñar. (1993) Global properties of zeros for Sobolev-type orthogonal polynomials. Journal of Computational and Applied Mathematics 49:1-3, pages 225-232.
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F. Marcellán, M. Alfaro & M.L. Rezola. (1993) Orthogonal polynomials on Sobolev spaces: old and new directions. Journal of Computational and Applied Mathematics 48:1-2, pages 113-131.
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R. Koekoek & H. G. Meijer. (1993) A Generalization of Laguerre Polynomials. SIAM Journal on Mathematical Analysis 24:3, pages 768-782.
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A. Ronveaux. (1992) Sobolev inner products and orthogonal polynomials of Sobolev type. Numerical Algorithms 3:1, pages 393-399.
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M. Alfaro, F. Marcellán, M. L. Rezola & A. Ronveaux. (1992) On Orthogonal Polynomials of Sobolev Type: Algebraic Properties and Zeros. SIAM Journal on Mathematical Analysis 23:3, pages 737-757.
Crossref
A Iserles, P.E Koch, S.P Nørsett & J.M Sanz-Serna. (1991) On polynomials orthogonal with respect to certain Sobolev inner products. Journal of Approximation Theory 65:2, pages 151-175.
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Roelof Koekoek. (1990) Generalizations of Laguerre polynomials. Journal of Mathematical Analysis and Applications 153:2, pages 576-590.
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H. Bavinck & H.G. Meijer. (1990) On orthogonal polynomials with respect to an inner product involving derivatives: zeros and recurrence relations. Indagationes Mathematicae 1:1, pages 7-14.
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