Sobolev orthogonal polynomials of high order in two variables defined on product domains

References

• Marcellán F, Alfaro M, Rezola ML. Orthogonal polynomials on Sobolev spaces: old and new directionst. J Comput Appl Math. 1993;48:113–131. doi: 10.1016/0377-0427(93)90318-6
   Web of Science ®Google Scholar
• Martínez-Finkelshtein A. Asymptotic properties of Sobolev orthogonal polynomials. J Comput Appl Math. 1998;99:491–510. doi: 10.1016/S0377-0427(98)00179-4
   Web of Science ®Google Scholar
• Martínez-Finkelshtein A. Analytic aspects of Sobolev orthogonal polynomials revisited. J Comput Appl Math. 2001;127:255–266. doi: 10.1016/S0377-0427(00)00499-4
   Web of Science ®Google Scholar
• Pérez TE, Piñar MA. On Sobolev orthogonality for the generalized Laguerre polynomials. J Approx Theory. 1996;86:278–285. doi: 10.1006/jath.1996.0069
   Web of Science ®Google Scholar
• Pérez TE, Piñar MA, Xu Y. Weighted Sobolev orthogonal polynomials on the unit ball. J Approx Theory. 2013;171:84–104. doi: 10.1016/j.jat.2013.03.004
   Web of Science ®Google Scholar
• Mello MV, Paschoa VC, Pérez TE, et al. Multivariate Sobolev-type orthogonal polynomials. Jaen J Approx. 2011;3(2):241–259.
   Google Scholar
• Marcellán F, Xu Y. On Sobolev orthogonal polynomials. Expo Math. 2015;33(3):308–352. doi: 10.1016/j.exmath.2014.10.002
   Web of Science ®Google Scholar
• Álvarez-Nodarse R, Marcellán F. A generalization of the classical Laguerre polynomials: asymptotic properties and Zeros. Appl Anal. 1996;62:349–366. doi: 10.1080/00036819608840488
   Google Scholar
• Àlvarez-Nodarse R, Moreno-Balcázar JJ. Asymptotic properties of generalized Laguerre orthogonal polynomials. Indag Math NS. 2004;15:151–165. doi: 10.1016/S0019-3577(04)90012-2
   Web of Science ®Google Scholar
• Deaño A, Huertas E, Marcellán F. Strong and ratio asymptotics for Laguerre polynomials revisited. J Math Anal Appl. 2013;403(2):477–486. doi: 10.1016/j.jmaa.2013.02.039
   Web of Science ®Google Scholar
• Dimitrov DK, Mello MV, Rafaeli FR. Monotonicity of zeros of Jacobi–Sobolev type orthogonal polynomials. Appl Numer Math. 2010;60(3):263–276. doi: 10.1016/j.apnum.2009.12.004
   Web of Science ®Google Scholar
• Dimitrov DK, Marcellán F, Rafaeli FR. Monotonicity of zeros of Laguerre Sobolev-type orthogonal polynomials. J Math Anal Appl. 2010;368(1):80–89. doi: 10.1016/j.jmaa.2010.02.038
   Web of Science ®Google Scholar
• Huertas E, Marcellán F, Rafaeli F. Zeros of orthogonal polynomials generated by canonical perturbations of measures. Appl Math Comput. 2012;8(13):7109–7127.
   Google Scholar
• Dueñas H, Marcellán F. The holonomic equation of the Laguerre–Sobolev-type orthogonal polynomials. A nondiagonal case. J Difference Equ Appl. 2011;17(6):877–887. doi: 10.1080/10236190903456063
   Web of Science ®Google Scholar
• Ismail MEH. An electrostatic model for zeros of general orthogonal polynomials. Pacific J Math. 2000;193:355–369. doi: 10.2140/pjm.2000.193.355
   Web of Science ®Google Scholar
• Dueñas H, Marcellán F. The Laguerre–Sobolev-type orthogonal polynomials. J Approx Theory. 2010;162:421–440. doi: 10.1016/j.jat.2009.07.006
   Web of Science ®Google Scholar
• Molano A. On asymptotic properties of Laguerre Sobolev type orthogonal polynomials. Arab J Math Sci. 2013;19(2):173–186.
   Google Scholar
• Dueñas H, Garza L, Piñar M. A higher order Sobolev-type inner product for orthogonal polynomials in several variables. Numer Algorithms. 2015;68(1):35–46. doi: 10.1007/s11075-014-9836-x
   Web of Science ®Google Scholar
• Fernández L, Marcellán F, Pérez T, et al. Sobolev orthogonal polynomials on product domains. J Comput Appl Math. 2015;284(15):202–215. doi: 10.1016/j.cam.2014.09.015
   Web of Science ®Google Scholar
• Dunkl C, Xu Y. Orthogonal polynomials of several variables. 2nd ed. Encyclopedia of Mathematics and its Applications 155. Cambridge: Cambridge University Press; 2014.
   Google Scholar
• De Jesus MN, Marcellán F, Petronilho J, et al. (M,N)-coherent pairs of order (m,k) and Sobolev orthogonal polynomials. J Comput Appl Math. 2014;256:16–35. doi: 10.1016/j.cam.2013.07.015
   Web of Science ®Google Scholar
• Marcellán F, Branquinho A, Petronilho J. Classical orthogonal polynomials: a functional approach. Acta Appl Math. 1994;34:283–303. doi: 10.1007/BF00998681
   Web of Science ®Google Scholar