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Vol. 15 Núm. 1 (2024)
Vol 15, Núm.1 (2024): Enero-Junio

Artículos de investigación / Research papers

Una nota sobre ceros de polinomios ortogonales generados por transformaciones canónicas

https://doi.org/10.19053/01217488.v15.n1.2024.15357

Publicado 2024-04-09

  • Luis Alejandro Molano Molano
    • ,
  • Germán Darío Cuida Plazas

Luis Alejandro Molano Molano


Germán Darío Cuida Plazas
Español

Resumen

En este trabajo se estudia el comportamiento de ceros de polinomios ortogonales asociados a transformaciones espectrales can\'{o}nicas de funciones de peso sobre $[0,\infty)$. A saber, mediante t\'{e}cnicas est\'{a}ndar, obtenemos propiedades de entrelazado para ceros asociados a algunos casos particulares de transformaciones racionales y de Christoffel.

Palabras clave

Polinomios Ortogonales, Transformaciones Canónicas, Ceros

Referencias

  • bibitem {dim}C.F. Bracciali, D.K. Dimitrov, A. Sri Ranga, "Chain sequences and
  • symmetric generalized orthogonal polynomials", J. Comput. Appl. Math. vol.143, pp.
  • --106, June 2002. https://doi.org/10.1016/S0377-0427(01)00499-X.
  • bibitem {branquimarc}A. Branquinho, F. Marcell'{a}n, "Generating new
  • classes of orthogonal polynomials", Int. J. Math. Math. Sci. vol. 19(4), pp. 643--656, 1996. DOI: 10.1155/S0161171296000919.
  • bibitem {brezQUASI}C. Brezinski, K. Driver, M. Redivo-Zaglia,
  • "Quasi-orthogonality 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.
  • bibitem {buenodea}M.I. Bueno, A. Dea~{n}o, E. Tavernetti, "A new algorithm
  • for computing the Geronimus transformation with large shifts", Numer. Alg. vol. 54,
  • pp. 101--139, May 2010. https://doi.org/10.1007/s11075-009-9325-9.
  • bibitem {buenoMarc}M.I. Bueno, F. Marcell'{a}n, "Darboux transformations and
  • perturbation of linear functionals", Linear Algebra Appl. vol. 384, pp. 215--242, June 2004. https://doi.org/10.1016/j.laa.2004.02.004
  • bibitem {chiha}T.S. Chihara, An introduction to Orthogonal Polynomials,
  • Gordon and Breach, New York, 1978.
  • bibitem {chris}E. B. Christoffel. ""{U}ber die Gaussische Quadratur und eine
  • Verallgemeinerung derselben", Journal f"{u}r die reine und angewandte
  • Mathematik, vol. 55, pp. 61-82, 1858. http://eudml.org/doc/147722.
  • bibitem {derMArce}M. Derevyagin, F. Marcell'{a}n, "A note on the Geronimus
  • transformation and Sobolev orthogonal polynomials", Numer. Algorithms, vol. 67, pp. 1--17, Octuber 2013. https://doi.org/10.1007/s11075-013-9788-6.
  • bibitem {elhai}S. Elhay, J. Kautsky, "Jacobi matrices for measures modified by
  • a rational factor", Numer. Algorithms, vol. 6, pp. 205-227, September 1994. https://doi.org/10.1007/BF02142672.
  • bibitem {feh}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, June 2011. https://doi.org/10.1007/BF03651367.
  • bibitem {fej2}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.
  • bibitem {Galant Rati}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.
  • bibitem {Galant Rati2}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.
  • bibitem {gautNum}W. Gautschi, Orthogonal Polynomials: Computation and
  • Approximation. Numerical Mathematics and Scientific Computation Series. Oxford
  • University Press, New York, 2004.
  • bibitem {GautRatio}W. Gautschi, "An algorithmic implementation of the
  • generalized Christoffel theorem", in: G. H"{a}mmerlin (Ed.), Numerical
  • Integration, Internat. Ser. Numer. Math., vol. 57, Birkh"{a}user, Basel,
  • pp. 89--106, 1982. https://doi.org/10.1007/978-3-0348-6308-7 9
  • bibitem {gero1}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.
  • bibitem {gero2}Ya.L. Geronimus, "On the polynomials orthogonal with respect to
  • a given number sequence and a theorem by W. Hahn", lzv. Akad. Nauk SSSR, vol. 4-2, pp. 215-228, 1940. http://mi.mathnet.ru/eng/izv/v4/i2/p215.
  • bibitem {huertas2}E. Huertas, F. Marcell'{a}n, 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.
  • bibitem {rafa}E. J. Huertas, F. Marcell'{a}n, F. R. Rafaeli, "Zeros of orthogonal polynomials generated by canonical
  • perturbations on measures", Appl. Math. Comput. vol. 218, pp. 7109--7127, March 2012. https://doi.org/10.1016/j.amc.2011.12.073.
  • bibitem {MAroniGero}P. Maroni, "Sur la suite de Polyn^{o}mes Orthogonaux Associ'{e}e `{a} la forme $u=delta(c)+lambda (x-c)^{-1}L$". Period. Math. Hungar. vol. 21(3), pp. 223--248, September 1990. https://doi.org/10.1007/bf02651091.
  • bibitem {spiri}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.
  • bibitem {shoatQUASI}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.
  • bibitem {sze}G. SzegH{o}, Orthogonal Polynomials, 4th ed.American
  • Mathematical Society Colloquim Publication Series, vol. 23, American
  • Mathematical Society, Providence, RI, 1975.
  • bibitem {Uva 1}V. B. Uvarov, "Relation between polynomials orthogonal with
  • different weights", (in Russian), Dokl. Akad. Nauk SSSR vol. 126, pp. 33--36, 1959.
  • bibitem {uva2}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.
  • bibitem {vanSecond}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.
  • bibitem {yoon}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.
  • bibitem {zedhanov}A. Zhedanov, "Rational spectral transformations and
  • orthogonal polynomials", J. Comput. Appl. Math. vol. 85, pp. 67--86, November 1997. https://doi.org/10.1016/S0377-0427(97)00130-1.

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