Zeros of Jacobi-Sobolev orthogonal polynomials following non-coherent pair of measures

被引：1
作者：
de Andrade E.X.L. [1 ]
Bracciali C.F. [1 ]
de Mello M.V. [1 ]
Pérez T.E. [2 ]
机构：
[1] DCCE, IBILCE, UNESP - Universidade Estadual Paulista, 15054-000 São José do Rio Preto, SP
[2] Departamento de Matemática Aplicada, Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada
来源：
Computational and Applied Mathematics | 2010年 / 29卷 / 03期
关键词：
Jacobi orthogonal polynomials; Sobolev orthogonal polynomials; Zeros of orthogonal polynomials;
D O I：
10.1590/S1807-03022010000300006
中图分类号：
学科分类号：
摘要：
Zeros of orthogonal polynomials associated with two different Sobolev inner products involving the Jacobi measure are studied. In particular, each of these Sobolev inner products involves a pair of closely related Jacobi measures. The measures of the inner products considered are beyond the concept of coherent pairs of measures. Existence, real character, location and interlacing properties for the zeros of these Jacobi-Sobolev orthogonal polynomials are deduced. © 2010 SBMAC.
引用
收藏
页码：423 / 445
页数：22
相关论文
共 15 条
  • [1] Andrade E.X.L., Bracciali C.F., Sri Ranga A., Zeros of Gegenbauer-Sobolev orthogonal polynomials: Beyond coherent pairs, Acta Appl. Math., 105, pp. 65-82, (2009)
  • [2] Berti A.C., Sri Ranga A., Companion orthogonal polynomials: Some applications, Appl. Numer. Math., 39, pp. 127-149, (2001)
  • [3] Berti A.C., Bracciali C.F., Sri Ranga A., Orthogonal polynomials associated with related measures and Sobolev orthogonal polynomials, Numer. Algorithms, 34, pp. 203-216, (2003)
  • [4] Bracciali C.F., Dimitrov D.K., Sri Ranga A., Chain sequences and symmetric generalized orthogonal polynomials, J. Comput. Appl. Math., 143, pp. 95-106, (2002)
  • [5] Chihara T.S., An Introduction to Orthogonal Polynomials, (1978)
  • [6] De Bruin M.G., Groenevelt W.G.M., Meijer H.G., Zeros of Sobolev orthogonal polynomials of Hermite type, Appl. Math. Comput., 132, pp. 135-166, (2002)
  • [7] Delgado A.M., Marcellan F., Companion linear functionals and Sobolev inner products: A case study, Methods Appl. Anal., 11, pp. 237-266, (2004)
  • [8] Groenevelt W.G.M., Zeros of Sobolev orthogonal polynomials of Gegenbauer type, J. Approx. Theory, 114, pp. 115-140, (2002)
  • [9] Iserles A., Koch P.E., Norsett S.P., Sanz-Serna J.M., On polynomialsorthogonal with respect to certain Sobolev inner products, J. Approx. Theory, 65, pp. 151-175, (1991)
  • [10] Kim D.H., Kwon K.H., Marcellan F., Yoon G.J., Zeros of Jacobi-Sobolev orthogonal polynomials, Int. Math. J., 4, 5, pp. 413-422, (2003)
12