A note on the Geronimus transformation and Sobolev orthogonal polynomials
In this note we recast the Geronimus transformation in the framework of polynomials orthogonal with respect to symmetric bilinear forms. We also show that the double Geronimus transformations lead to non-diagonal Sobolev type inner products.
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| Published in: | Numerical algorithms Vol. 67; no. 2; pp. 271 - 287 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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01-10-2014
Springer Nature B.V |
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| Abstract | In this note we recast the Geronimus transformation in the framework of polynomials orthogonal with respect to symmetric bilinear forms. We also show that the double Geronimus transformations lead to non-diagonal Sobolev type inner products. |
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| AbstractList | In this note we recast the Geronimus transformation in the framework of polynomials orthogonal with respect to symmetric bilinear forms. We also show that the double Geronimus transformations lead to non-diagonal Sobolev type inner products. |
| Author | Marcellán, Francisco Derevyagin, Maxim |
| Author_xml | – sequence: 1 givenname: Maxim surname: Derevyagin fullname: Derevyagin, Maxim email: derevyagin.m@gmail.com organization: Department of Mathematics MA 4-2, Technische Universität Berlin, Department of Mathematics, KU Leuven – sequence: 2 givenname: Francisco surname: Marcellán fullname: Marcellán, Francisco organization: Departamento de Matemáticas, Universidad Carlos III de Madrid |
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| Cites_doi | 10.1016/S0377-0427(97)00130-1 10.1137/S0036141092226922 10.1007/BF02651091 10.1088/0305-4470/30/24/031 10.1016/j.cam.2009.02.060 10.1016/j.jat.2013.04.002 10.1006/jath.1993.1055 10.1007/s10231-001-8200-7 10.1016/j.cam.2005.06.026 10.1090/S0002-9947-1937-1501930-6 10.1155/S0161171296000919 10.1016/S0168-9274(02)00250-7 10.1137/0523038 10.1016/S0377-0427(97)00227-6 10.1016/j.laa.2011.05.035 10.1016/j.laa.2005.09.010 10.1016/j.camwa.2010.12.037 10.1016/j.laa.2004.02.004 10.1007/s10231-011-0219-9 10.4310/MAA.1995.v2.n4.a1 10.4310/MAA.2000.v7.n4.a9 |
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| Keywords | Geronimus transformation Cholesky decomposition Sobolev inner products Secondary 15A23 Orthogonal polynomials Jacobi matrices Primary 42C05 |
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| References | Beghdadi, Maroni (CR4) 1998; 88 Iliev (CR16) 2013; 192 Bueno, Marcellán (CR7) 2004; 384 Kwon, Lee, Marcellán, Park (CR17) 2001; 180 CR6 Maroni, Nicolau (CR19) 2003; 45 Shohat (CR21) 1937; 42 Alfaro, Marcellán, Peña, Rezola (CR2) 2010; 233 Geronimus (CR14) 1940; 17 CR9 Derevyagin, Derkach (CR11) 2011; 435 Branquinho, Marcellán (CR5) 1996; 19 Hounga, Hounkonnou, Ronveaux (CR15) 2006; 193 Derevyagin (CR10) 2013; 172 Bueno, Marcellán (CR8) 2006; 414 Alfaro, Marcellán, Rezola, Ronveaux (CR1) 1992; 23 Zhedanov (CR24) 1997; 85 Spiridonov, Zhedanov (CR23) 1997; 30 Maroni (CR18) 1990; 21 Maroni, Sfaxi (CR20) 2000; 7 Spiridonov, Zhedanov (CR22) 1995; 2 Alfaro, Peña, Rezola, Marcellán (CR3) 2011; 61 Durán (CR12) 1993; 74 Evans, Littlejohn, Marcellán, Markett, Ronveaux (CR13) 1995; 26 P Maroni (9788_CR19) 2003; 45 V Spiridonov (9788_CR22) 1995; 2 MI Bueno (9788_CR8) 2006; 414 9788_CR9 D Evans (9788_CR13) 1995; 26 M Derevyagin (9788_CR10) 2013; 172 J Geronimus (9788_CR14) 1940; 17 9788_CR6 D Beghdadi (9788_CR4) 1998; 88 A Branquinho (9788_CR5) 1996; 19 MI Bueno (9788_CR7) 2004; 384 M Alfaro (9788_CR3) 2011; 61 AJ Durán (9788_CR12) 1993; 74 A Zhedanov (9788_CR24) 1997; 85 P Maroni (9788_CR20) 2000; 7 J Shohat (9788_CR21) 1937; 42 M Alfaro (9788_CR1) 1992; 23 M Derevyagin (9788_CR11) 2011; 435 P Maroni (9788_CR18) 1990; 21 KH Kwon (9788_CR17) 2001; 180 V Spiridonov (9788_CR23) 1997; 30 M Alfaro (9788_CR2) 2010; 233 P Iliev (9788_CR16) 2013; 192 C Hounga (9788_CR15) 2006; 193 |
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| Title | A note on the Geronimus transformation and Sobolev orthogonal polynomials |
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