"Koornwinder polynomials"의 두 판 사이의 차이
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* The Koornwinder polynomials [43] are a generalisation of the [[Macdonald polynomials]] to the root system BCn. | * The Koornwinder polynomials [43] are a generalisation of the [[Macdonald polynomials]] to the root system BCn. | ||
* They depend on six parameters, except for n = 1 when they correspond to the 5-parameter Askey–Wilson polynomials [3]. | * They depend on six parameters, except for n = 1 when they correspond to the 5-parameter Askey–Wilson polynomials [3]. | ||
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| + | ==history== | ||
| + | * Several years after the work of Askey and Wilson, Koornwinder extended the Askey–Wilson polynomials to a family of multivariable Laurent polynomials labelled by the non-reduced root system $BC_n$ | ||
| + | * The various families of Macdonald (orthogonal) polynomials for classical root systems are all contained in the Koornwinder polynomials, and for a long time it was assumed they represented the highest possible level of generalisation. | ||
2015년 8월 3일 (월) 18:13 판
introduction
- The Koornwinder polynomials [43] are a generalisation of the Macdonald polynomials to the root system BCn.
- They depend on six parameters, except for n = 1 when they correspond to the 5-parameter Askey–Wilson polynomials [3].
history
- Several years after the work of Askey and Wilson, Koornwinder extended the Askey–Wilson polynomials to a family of multivariable Laurent polynomials labelled by the non-reduced root system $BC_n$
- The various families of Macdonald (orthogonal) polynomials for classical root systems are all contained in the Koornwinder polynomials, and for a long time it was assumed they represented the highest possible level of generalisation.
articles
- Corteel, Sylvie, and Lauren Williams. ‘Macdonald-Koornwinder Moments and the Two-Species Exclusion Process’. arXiv:1505.00843 [cond-Mat, Physics:nlin], 4 May 2015. http://arxiv.org/abs/1505.00843.
- Stokman, Jasper V. “Lecture Notes on Koornwinder Polynomials.” In Laredo Lectures on Orthogonal Polynomials and Special Functions, 145–207. Adv. Theory Spec. Funct. Orthogonal Polynomials. Nova Sci. Publ., Hauppauge, NY, 2004. http://www.ams.org/mathscinet-getitem?mr=2085855.
- Stokman, Jasper V. “Macdonald-Koornwinder Polynomials.” arXiv:1111.6112 [math], November 25, 2011. http://arxiv.org/abs/1111.6112.
- [43] T. H. Koornwinder, Askey–Wilson polynomials for root systems of type BC in Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications, pp. 189–204, Contemp. Math. 138, Amer. Math. Soc., Providence, 1992.
- [3] R. Askey and J. A. Wilson, Some basic hypergeometric polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. Vol. 319, AMS, Providence, RI, 1985.