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Keywords:
Dunkl Laplacian; Dunkl Ornstein-Uhlenbeck operator; generalized Hermite polynomial; Riesz transform
Summary:
The aim of this paper is to extend the study of Riesz transforms associated to Dunkl Ornstein-Uhlenbeck operator considered by A. Nowak, L. Roncal and K. Stempak to higher order.
References:
[1] Chihara, T. S.: Generalized Hermite Polynomials. Thesis (Ph.D.). Purdue University, West Lafayette (1955). MR 2612324
[2] Dunkl, C. D.: Differential-difference operators associated to reflection groups. Trans. Am. Math. Soc. 311 (1989), 167-183. DOI 10.2307/2001022 | MR 0951883 | Zbl 0652.33004
[3] Graczyk, P., Loeb, J. J., López, I., Nowak, A., Urbina, W.: Higher order Riesz transforms, fractional derivatives, and Sobolev spaces for Laguerre expansions. J. Math. Pures Appl. 84 (2005), 375-405. DOI 10.1016/j.matpur.2004.09.003 | MR 2121578 | Zbl 1129.42015
[4] Lebedev, N. N.: Special Functions and Their Applications. Dover Publications, New York (1972). MR 0350075 | Zbl 0271.33001
[5] Muckenhoupt, B.: Conjugate functions for Laguerre expansions. Trans. Am. Math. Soc. 147 (1970), 403-418. DOI 10.2307/1995203 | MR 0252945 | Zbl 0192.46202
[6] Nefzi, W.: Higher order Riesz transforms for the Dunkl harmonic oscillator. Taiwanese J. Math. 19 (2015), 567-583. DOI 10.11650/tjm.19.2015.4762 | MR 3332314 | Zbl 1357.42006
[7] Nowak, A., Roncal, L., Stempak, K.: Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator. Colloq. Math. 118 (2010), 669-684. DOI 10.4064/cm118-2-19 | MR 2602173 | Zbl 1194.42036
[8] Nowak, A., Stempak, K.: Riesz transforms for the Dunkl harmonic oscillator. Math. Z. 262 (2009), 539-556. DOI 10.1007/s00209-008-0388-4 | MR 2506306 | Zbl 1168.44002
[9] Rosenblum, M.: Generalized Hermite polynomials and the Bose-like oscillator calculus. Nonselfadjoint Operators and Related Topics A. Feintuch et al. Operator Theory: Advances and Applications 73, Birkhäuser, Basel (1994), 369-396. MR 1320555 | Zbl 0826.33005
[10] Rösler, M.: Generalized Hermite polynomials and the heat equation for Dunkl operators. Commun. Math. Phys. 192 (1998), 519-542. DOI 10.1007/s002200050307 | MR 1620515 | Zbl 0908.33005
[11] Rösler, M.: Dunkl operators: Theory and applications. E. Koelink et al. Orthogonal Polynomials and Special Functions Lecture Notes in Mathematics 1817, Springer, Berlin (2003), 93-135. DOI 10.1007/3-540-44945-0_3 | MR 2022853 | Zbl 1029.43001
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