A note on zeros of orthogonal polynomials generated by canonical transformations
- Autores:
-
Molano, Luis Alejandro Molano
Cuida Plazas, Germán Darío
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2024
- Institución:
- Universidad Pedagógica y Tecnológica de Colombia
- Repositorio:
- RiUPTC: Repositorio Institucional UPTC
- Idioma:
- OAI Identifier:
- oai:repositorio.uptc.edu.co:001/18722
- Acceso en línea:
- https://repositorio.uptc.edu.co/handle/001/18722
https://doi.org/10.19053/01217488.v15.n1.2024.15357
- Palabra clave:
- Polinomios Ortogonales
Transformaciones Canónicas
Ceros
Orthogonal polynomials
Canonical transformations
Zeros
- Rights
- openAccess
- License
- https://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
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A note on zeros of orthogonal polynomials generated by canonical transformations |
| title |
A note on zeros of orthogonal polynomials generated by canonical transformations |
| spellingShingle |
A note on zeros of orthogonal polynomials generated by canonical transformations Polinomios Ortogonales Transformaciones Canónicas Ceros Orthogonal polynomials Canonical transformations Zeros |
| title_short |
A note on zeros of orthogonal polynomials generated by canonical transformations |
| title_full |
A note on zeros of orthogonal polynomials generated by canonical transformations |
| title_fullStr |
A note on zeros of orthogonal polynomials generated by canonical transformations |
| title_full_unstemmed |
A note on zeros of orthogonal polynomials generated by canonical transformations |
| title_sort |
A note on zeros of orthogonal polynomials generated by canonical transformations |
| dc.creator.fl_str_mv |
Molano, Luis Alejandro Molano Cuida Plazas, Germán Darío |
| dc.contributor.author.spa.fl_str_mv |
Molano, Luis Alejandro Molano Cuida Plazas, Germán Darío |
| dc.subject.none.fl_str_mv |
Polinomios Ortogonales Transformaciones Canónicas Ceros Orthogonal polynomials Canonical transformations Zeros |
| topic |
Polinomios Ortogonales Transformaciones Canónicas Ceros Orthogonal polynomials Canonical transformations Zeros |
| publishDate |
2024 |
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2024-10-15 11:19:25 2026-04-16T17:12:22Z |
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2024-10-15 11:19:25 |
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2024-10-15 |
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E. B. Christoffel, “U¨ ber die Gaussische Quadratur und eine Verallgemeinerung derselben”, Journal f¨ur die reine und angewandte Mathematik, vol. 55, pp. 61-82, 1858. http://eudml.org/doc/147722. T.S. Chihara, An introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978. G. Szeg˝o, Orthogonal Polynomials, 4th ed.American Mathematical Society Colloquim Publication Series, vol. 23, American Mathematical Society, Providence, RI, 1975. G.J. Yoon, “Darboux transforms and orthogonal polynomials”, Bull. Korean Math. Soc. vol. 39, pp. 359– 376, 2002. https://doi.org/10.4134/BKMS.2002.39.3. 359. S. Elhay, J. Kautsky, “Jacobi matrices for measures modified by a rational factor”, Numer. Algorithms, vol. 6, pp. 205-227, 1994. https://doi.org/10.1007/ BF02142672. B. X. Fejzullahu,R. X. Zejnullahu, “Orthogonal polynomials with respect to the Laguerre measure perturbed by the canonical transformations”, Integ. Transf. Spec. Funct. vol. 21, pp. 569-580, 2010. https://doi. org/10.1080/10652460903442032. E. Huertas, F. Marcell´an, B. Xh. Fejnullahu, R.Xh. Zejnullahu, “On orthogonal polynomials with respect to certain discrete Sobolev inner product”, Pacific J. Math. vol. 257-1, pp. 167-188, 2012. DOI: 10.2140/pjm.2012.257.167. E. J. Huertas, F. Marcell´an, F. R. Rafaeli, “Zeros of orthogonal polynomials generated by canonical perturbations on measures”, Appl. Math. Comput. vol. 218, pp. 7109–7127, 2012. https://doi.org/10.1016/j.amc. 2011.12.073. V. B. Uvarov, “Relation between polynomials orthogonal with different weights”, (in Russian), Dokl. Akad. Nauk SSSR vol. 126, pp. 33–36, 1959. V. B. Uvarov, “The connection between systems of polynomials that are orthogonal with respect to different distributionfunctions”, (in Russian), Z. Vycisl. Mat. i Mat. Fiz. vol. 9, pp. 1253–1262, 1969. [English translation in USSR Comput. Math. Math. Phys. vol. 9, pp. 25–36, 1969]. https://doi.org/10.1016/0041-5553(69)90124-4. A. Zhedanov, “Rational spectral transformations and orthogonal polynomials”, J. Comput. Appl. Math. vol. 85, pp. 67–86, 1997. https://doi.org/10.1016/S0377-0427(97)00130-1. Ya.L. Geronimus, “On the polynomials orthogonal with respect to a given number sequence”, Zap. Mat. Otdel. Khar’kov. Univers. i NII Mat. i Mehan. vol. 17, pp. 3-18, 1940. Ya.L. Geronimus, “On the polynomials orthogonal with respect to a given number sequence and a theorem byW. Hahn”, lzv. Akad. Nauk SSSR, vol. 4-2, pp. 215-228, 1940. http://mi.mathnet.ru/eng/izv/v4/i2/p215. A. Branquinho, F. Marcell´an, “Generating new classes of orthogonal polynomials”, Int. J. Math. Math. Sci. vol. 19(4), pp. 643–656, 1996. DOI: 10.1155/S0161171296000919. M.I. Bueno, A. Dea˜no, E. Tavernetti, “A new algorithm for computing the Geronimus transformation with large shifts”, Numer. Alg. vol. 54, pp. 101–139, 2010. https://doi.org/10.1007/s11075-009-9325-9. M.I. Bueno, F. Marcell´an, “Darboux transformations and perturbation of linear functionals”, Linear Algebra Appl. vol. 384, pp. 215–242, 2004. https://doi.org/10.1016/j.laa.2004.02.004 M. Derevyagin, F. Marcell´an, “A note on the Geronimus transformation and Sobolev orthogonal polynomials”, Numer. Algorithms, vol. 67, pp. 1–17, 2013. https://doi.org/10.1007/s11075-013-9788-6. W. Gautschi, Orthogonal Polynomials: Computation and Approximation. Numerical Mathematics and Scientific Computation Series. Oxford University Press, New York, 2004. P. Maroni, “Sur la suite de Polynˆomes Orthogonaux Associ´ee `a la forme u = δ(c)+λ(x−c)−1L”. Period. Math. Hungar. vol. 21(3), pp. 223–248, 1990. https://doi.org/10.1007/bf02651091. V. Spiridonov, A. Zhedanov, “Discrete-time Volterra chain and classical orthogonal polynomials”, J. Phys. A. Math. Gen. vol. 30-24, pp. 8727–8737, 1997. DOI 10.1088/0305-4470/30/24/031. B. X. Fejzullahu, “Asymptotics for orthogonal polynomials with respect to the Laguerre measure modified by a rational factor”, Acta Sci. Math. .Szeged. vol. 77, pp. 73–85, 2011. https://doi.org/10.1007/BF03651367. D. Galant, “An implementation of Christoffel’s theorem in the theory of orthogonal polynomials”, Math. Comp. vol. 25, pp. 111–113, 1979. DOI:10.1090/S0025-5718-1971-0288954-8. D. Galant, “Algebraic methods for modified orthogonal polynomials”, Math. Comp. 59, pp. 541–546, 1992. DOI: https://doi.org/10.1090/S0025-5718-1992-1140648-6. W. Gautschi, “An algorithmic implementation of the generalized Christoffel theorem”, in: G. H¨ammerlin (Ed.), Numerical Integration, Internat. Ser. Numer. Math., vol. 57, Birkh¨auser, Basel, pp. 89–106, 1982. https://doi.org/10.1007/978-3-0348-6308-79 C.F. Bracciali, D.K. Dimitrov, A. Sri Ranga, “Chain sequences and symmetric generalized orthogonal polynomials”, J. Comput. Appl. Math. vol.143, pp. 95- 106, 2002. https://doi.org/10.1016/S0377-0427(01)00499-X. C. Brezinski, K. Driver, M. Redivo-Zaglia, ”Quasiorthogonality with applications to some families of classical orthogonal polynomials”, Appl. Numer. Math. vol. 48, pp. 157–168, February 2004. https://doi.org/ 10.1016/j.apnum.2003.10.001. J.A. Shohat, .On mechanical quadratures, in particular, with positive coefficients”, Trans. Amer. Math. Soc. vol 42-3, pp. 461–496, November 1937. https://doi.org/10.2307/1989740. W. Van Assche, .Orthogonal polynomials, associated polynomials and functions of the second kind”, J. Comput. Appl. Math. vol. 37, pp. 237-249, November 1991. https://doi.org/10.1016/0377-0427(91)90121-Y. |
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Molano, Luis Alejandro MolanoCuida Plazas, Germán Darío2024-10-15 11:19:252026-04-16T17:12:22Z2024-10-15 11:19:252024-10-150121-7488https://repositorio.uptc.edu.co/handle/001/1872210.19053/01217488.v15.n1.2024.153572462-7658https://doi.org/10.19053/01217488.v15.n1.2024.15357application/pdfUniversidad Pedagógica y Tecnológica de Colombiahttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.esinfo:eu-repo/semantics/openAccessEsta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-SinDerivadas 4.0.http://purl.org/coar/access_right/c_abf2https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/15357Polinomios OrtogonalesTransformaciones CanónicasCerosOrthogonal polynomialsCanonical transformationsZerosA note on zeros of orthogonal polynomials generated by canonical transformationsArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1info:eu-repo/semantics/articleJournal articleinfo:eu-repo/semantics/publishedVersionTexthttp://purl.org/coar/version/c_970fb48d4fbd8a85E. B. Christoffel, “U¨ ber die Gaussische Quadratur und eine Verallgemeinerung derselben”, Journal f¨ur die reine und angewandte Mathematik, vol. 55, pp. 61-82, 1858. http://eudml.org/doc/147722.T.S. Chihara, An introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978.G. Szeg˝o, Orthogonal Polynomials, 4th ed.American Mathematical Society Colloquim Publication Series, vol. 23, American Mathematical Society, Providence, RI, 1975.G.J. Yoon, “Darboux transforms and orthogonal polynomials”, Bull. Korean Math. Soc. vol. 39, pp. 359– 376, 2002. https://doi.org/10.4134/BKMS.2002.39.3. 359.S. Elhay, J. Kautsky, “Jacobi matrices for measures modified by a rational factor”, Numer. Algorithms, vol. 6, pp. 205-227, 1994. https://doi.org/10.1007/ BF02142672.B. X. Fejzullahu,R. X. Zejnullahu, “Orthogonal polynomials with respect to the Laguerre measure perturbed by the canonical transformations”, Integ. Transf. Spec. Funct. vol. 21, pp. 569-580, 2010. https://doi. org/10.1080/10652460903442032.E. Huertas, F. Marcell´an, B. Xh. Fejnullahu, R.Xh. Zejnullahu, “On orthogonal polynomials with respect to certain discrete Sobolev inner product”, Pacific J. Math. vol. 257-1, pp. 167-188, 2012. DOI: 10.2140/pjm.2012.257.167.E. J. Huertas, F. Marcell´an, F. R. Rafaeli, “Zeros of orthogonal polynomials generated by canonical perturbations on measures”, Appl. Math. Comput. vol. 218, pp. 7109–7127, 2012. https://doi.org/10.1016/j.amc. 2011.12.073.V. B. Uvarov, “Relation between polynomials orthogonal with different weights”, (in Russian), Dokl. Akad. Nauk SSSR vol. 126, pp. 33–36, 1959.V. B. Uvarov, “The connection between systems of polynomials that are orthogonal with respect to different distributionfunctions”, (in Russian), Z. Vycisl. Mat. i Mat. Fiz. vol. 9, pp. 1253–1262, 1969. [English translation in USSR Comput. Math. Math. Phys. vol. 9, pp. 25–36, 1969]. https://doi.org/10.1016/0041-5553(69)90124-4.A. Zhedanov, “Rational spectral transformations and orthogonal polynomials”, J. Comput. Appl. Math. vol. 85, pp. 67–86, 1997. https://doi.org/10.1016/S0377-0427(97)00130-1.Ya.L. Geronimus, “On the polynomials orthogonal with respect to a given number sequence”, Zap. Mat. Otdel. Khar’kov. Univers. i NII Mat. i Mehan. vol. 17, pp. 3-18, 1940.Ya.L. Geronimus, “On the polynomials orthogonal with respect to a given number sequence and a theorem byW. Hahn”, lzv. Akad. Nauk SSSR, vol. 4-2, pp. 215-228, 1940. http://mi.mathnet.ru/eng/izv/v4/i2/p215.A. Branquinho, F. Marcell´an, “Generating new classes of orthogonal polynomials”, Int. J. Math. Math. Sci. vol. 19(4), pp. 643–656, 1996. DOI: 10.1155/S0161171296000919.M.I. Bueno, A. Dea˜no, E. Tavernetti, “A new algorithm for computing the Geronimus transformation with large shifts”, Numer. Alg. vol. 54, pp. 101–139, 2010. https://doi.org/10.1007/s11075-009-9325-9.M.I. Bueno, F. Marcell´an, “Darboux transformations and perturbation of linear functionals”, Linear Algebra Appl. vol. 384, pp. 215–242, 2004. https://doi.org/10.1016/j.laa.2004.02.004M. Derevyagin, F. Marcell´an, “A note on the Geronimus transformation and Sobolev orthogonal polynomials”, Numer. Algorithms, vol. 67, pp. 1–17, 2013. https://doi.org/10.1007/s11075-013-9788-6.W. Gautschi, Orthogonal Polynomials: Computation and Approximation. Numerical Mathematics and Scientific Computation Series. Oxford University Press, New York, 2004.P. Maroni, “Sur la suite de Polynˆomes Orthogonaux Associ´ee `a la forme u = δ(c)+λ(x−c)−1L”. Period. Math. Hungar. vol. 21(3), pp. 223–248, 1990. https://doi.org/10.1007/bf02651091.V. Spiridonov, A. Zhedanov, “Discrete-time Volterra chain and classical orthogonal polynomials”, J. Phys. A. Math. Gen. vol. 30-24, pp. 8727–8737, 1997. DOI 10.1088/0305-4470/30/24/031.B. X. Fejzullahu, “Asymptotics for orthogonal polynomials with respect to the Laguerre measure modified by a rational factor”, Acta Sci. Math. .Szeged. vol. 77, pp. 73–85, 2011. https://doi.org/10.1007/BF03651367.D. Galant, “An implementation of Christoffel’s theorem in the theory of orthogonal polynomials”, Math. Comp. vol. 25, pp. 111–113, 1979. DOI:10.1090/S0025-5718-1971-0288954-8.D. Galant, “Algebraic methods for modified orthogonal polynomials”, Math. Comp. 59, pp. 541–546, 1992. DOI: https://doi.org/10.1090/S0025-5718-1992-1140648-6.W. Gautschi, “An algorithmic implementation of the generalized Christoffel theorem”, in: G. H¨ammerlin (Ed.), Numerical Integration, Internat. Ser. Numer. Math., vol. 57, Birkh¨auser, Basel, pp. 89–106, 1982. https://doi.org/10.1007/978-3-0348-6308-79C.F. Bracciali, D.K. Dimitrov, A. Sri Ranga, “Chain sequences and symmetric generalized orthogonal polynomials”, J. Comput. Appl. Math. vol.143, pp. 95- 106, 2002. https://doi.org/10.1016/S0377-0427(01)00499-X.C. Brezinski, K. Driver, M. Redivo-Zaglia, ”Quasiorthogonality with applications to some families of classical orthogonal polynomials”, Appl. Numer. Math. vol. 48, pp. 157–168, February 2004. https://doi.org/ 10.1016/j.apnum.2003.10.001.J.A. Shohat, .On mechanical quadratures, in particular, with positive coefficients”, Trans. Amer. Math. Soc. vol 42-3, pp. 461–496, November 1937. https://doi.org/10.2307/1989740.W. Van Assche, .Orthogonal polynomials, associated polynomials and functions of the second kind”, J. Comput. Appl. Math. vol. 37, pp. 237-249, November 1991. https://doi.org/10.1016/0377-0427(91)90121-Y.149114115Ciencia en Desarrollohttps://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/download/15357/14433Núm. 1 , Año 2024 : Vol 15, Núm.1 (2024): Enero-JunioPublicationOREORE.xmltext/xml2675https://repositorio.uptc.edu.co/bitstreams/af07380c-691c-4b10-b926-36a22feea657/download98d0b673ada0ea91a5fff03ababa6191MD51falseAnonymousREAD001/18722oai:repositorio.uptc.edu.co:001/187222026-10-30 07:02:33.672https://creativecommons.org/licenses/by-nc-nd/4.0/deed.esmetadata.onlyhttps://repositorio.uptc.edu.coRepositorio Institucional UPTCbdigital@metabiblioteca.com |