Chea, Vutha Vichhea; Vinet, Luc; Zaimi, Meri; Zhedanov, Alexei An algebraic treatment of the Pastro polynomials on the real line. (English) Zbl 07741070 Proc. Am. Math. Soc. 151, No. 10, 4405-4418 (2023). MSC: 39A13 39A70 33D45 47B36 05A30 PDFBibTeX XMLCite \textit{V. V. Chea} et al., Proc. Am. Math. Soc. 151, No. 10, 4405--4418 (2023; Zbl 07741070) Full Text: DOI arXiv
Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei The rational Heun operator and Wilson biorthogonal functions. (English) Zbl 07690247 Ramanujan J. 61, No. 1, 7-29 (2023). MSC: 33D45 33C47 47B36 42C05 39A70 39A13 PDFBibTeX XMLCite \textit{S. Tsujimoto} et al., Ramanujan J. 61, No. 1, 7--29 (2023; Zbl 07690247) Full Text: DOI arXiv
Miki, Hiroshi; Tsujimoto, Satoshi; Vinet, Luc The single-indexed exceptional Krawtchouk polynomials. (English) Zbl 07686655 J. Difference Equ. Appl. 29, No. 3, 344-365 (2023). Reviewer: Ahmad Barhoumi (Stockholm) MSC: 33C45 44A55 39A70 PDFBibTeX XMLCite \textit{H. Miki} et al., J. Difference Equ. Appl. 29, No. 3, 344--365 (2023; Zbl 07686655) Full Text: DOI arXiv
Baseilhac, Pascal; Vinet, Luc; Zhedanov, Alexei The q-Heun operator of big q-Jacobi type and the q-Heun algebra. (English) Zbl 1444.39007 Ramanujan J. 52, No. 2, 367-380 (2020). Reviewer: Lalit Mohan Upadhyaya (Mussoorie) MSC: 39A13 39A70 33D05 33E30 33C45 PDFBibTeX XMLCite \textit{P. Baseilhac} et al., Ramanujan J. 52, No. 2, 367--380 (2020; Zbl 1444.39007) Full Text: DOI arXiv
Baseilhac, Pascal; Martin, Xavier; Vinet, Luc; Zhedanov, Alexei Little and big \(q\)-Jacobi polynomials and the Askey-Wilson algebra. (English) Zbl 1436.81070 Ramanujan J. 51, No. 3, 629-648 (2020). MSC: 81R50 81R10 81U15 39A70 33D50 39A13 17B37 PDFBibTeX XMLCite \textit{P. Baseilhac} et al., Ramanujan J. 51, No. 3, 629--648 (2020; Zbl 1436.81070) Full Text: DOI arXiv
Vinet, Luc; Zhedanov, Alexei The Heun operator of Hahn-type. (English) Zbl 1429.33018 Proc. Am. Math. Soc. 147, No. 7, 2987-2998 (2019). Reviewer: Manuel D. de la Iglesia (México D. F.) MSC: 33C45 33C80 39A70 PDFBibTeX XMLCite \textit{L. Vinet} and \textit{A. Zhedanov}, Proc. Am. Math. Soc. 147, No. 7, 2987--2998 (2019; Zbl 1429.33018) Full Text: DOI arXiv
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei Algebraic Heun operator and band-time limiting. (English) Zbl 1405.33025 Commun. Math. Phys. 364, No. 3, 1041-1068 (2018). Reviewer: Chrysoula G. Kokologiannaki (Patras) MSC: 33D45 33D99 39B42 PDFBibTeX XMLCite \textit{F. A. Grünbaum} et al., Commun. Math. Phys. 364, No. 3, 1041--1068 (2018; Zbl 1405.33025) Full Text: DOI arXiv
Gaboriaud, Julien; Genest, Vincent X.; Lemieux, Jessica; Vinet, Luc A superintegrable discrete oscillator and two-variable Meixner polynomials. (English) Zbl 1326.81090 J. Phys. A, Math. Theor. 48, No. 41, Article ID 415202, 14 p. (2015). MSC: 81Q80 33C80 39A14 33C50 PDFBibTeX XMLCite \textit{J. Gaboriaud} et al., J. Phys. A, Math. Theor. 48, No. 41, Article ID 415202, 14 p. (2015; Zbl 1326.81090) Full Text: DOI arXiv
Vinet, Luc; Yu, Guo-Fu; Zhang, Ying-Nan On an integrable system related to the relativistic Toda lattice – Bäcklund transformation and integrable discretization. (English) Zbl 1320.37033 J. Difference Equ. Appl. 21, No. 5, 403-417 (2015). MSC: 37K10 39A70 37K60 PDFBibTeX XMLCite \textit{L. Vinet} et al., J. Difference Equ. Appl. 21, No. 5, 403--417 (2015; Zbl 1320.37033) Full Text: DOI arXiv
Genest, Vincent X.; Miki, Hiroshi; Vinet, Luc; Yu, Guofu A superintegrable discrete harmonic oscillator based on bivariate Charlier polynomials. arXiv:1511.09155 Preprint, arXiv:1511.09155 [math-ph] (2015). MSC: 39A14 39A70 37K05 70H33 81R12 81R05 BibTeX Cite \textit{V. X. Genest} et al., ``A superintegrable discrete harmonic oscillator based on bivariate Charlier polynomials'', Preprint, arXiv:1511.09155 [math-ph] (2015) Full Text: arXiv OA License
Miki, Hiroshi; Post, Sarah; Vinet, Luc; Zhedanov, Alexei A superintegrable finite oscillator in two dimensions with \(SU(2)\) symmetry. (English) Zbl 1266.39011 J. Phys. A, Math. Theor. 46, No. 12, Article ID 125207, 13 p. (2013). MSC: 39A14 39A70 39A12 37K05 70H33 81R12 PDFBibTeX XMLCite \textit{H. Miki} et al., J. Phys. A, Math. Theor. 46, No. 12, Article ID 125207, 13 p. (2013; Zbl 1266.39011) Full Text: DOI arXiv
Vinet, Luc; Zhedanov, Alexei Generalized Bochner theorem: Characterization of the Askey-Wilson polynomials. (English) Zbl 1140.33006 J. Comput. Appl. Math. 211, No. 1, 45-56 (2008). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 33D45 42C05 39A10 PDFBibTeX XMLCite \textit{L. Vinet} and \textit{A. Zhedanov}, J. Comput. Appl. Math. 211, No. 1, 45--56 (2008; Zbl 1140.33006) Full Text: DOI arXiv
Vinet, Luc; Zhedanov, Alexei Generalized little \(q\)-Jacobi polynomials as eigensolutions of higher-order \(q\)-difference operators. (English) Zbl 0973.33009 Proc. Am. Math. Soc. 129, No. 5, 1317-1327 (2001). Reviewer: Roelof Koekoek (Delft) MSC: 33D45 39A13 PDFBibTeX XMLCite \textit{L. Vinet} and \textit{A. Zhedanov}, Proc. Am. Math. Soc. 129, No. 5, 1317--1327 (2001; Zbl 0973.33009) Full Text: DOI
Vinet, Luc; Zhedanov, Alexei An integrable system connected with the Uvarov-Chihara problem for orthogonal polynomials. (English) Zbl 0942.42017 J. Phys. A, Math. Gen. 31, No. 47, 9579-9591 (1998). MSC: 42C05 37J35 39A12 33C45 82C20 PDFBibTeX XMLCite \textit{L. Vinet} and \textit{A. Zhedanov}, J. Phys. A, Math. Gen. 31, No. 47, 9579--9591 (1998; Zbl 0942.42017) Full Text: DOI
Spiridonov, Vyacheslav; Vinet, Luc; Zhedanov, Alexei Bispectrality and Darboux transformations in the theory of orthogonal polynomials. (English) Zbl 0901.42015 Harnad, John (ed.) et al., The bispectral problem. Proceedings of the CRM workshop, Montréal, Canada, March 1997. Providence, RI: American Mathematical Society. CRM Proc. Lect. Notes. 14, 111-122 (1998). Reviewer: M.G.de Bruin (Delft) MSC: 42C05 33C45 47B39 39A10 PDFBibTeX XMLCite \textit{V. Spiridonov} et al., in: The bispectral problem. Proceedings of the CRM workshop, Montréal, Canada, March 1997. Providence, RI: American Mathematical Society. 111--122 (1998; Zbl 0901.42015)
Levi, D.; Vinet, L.; Winternitz, P. Lie group formalism for difference equations. (English) Zbl 0956.39013 J. Phys. A, Math. Gen. 30, No. 2, 633-649 (1997). Reviewer: Patricia J.Y.Wong (Singapore) MSC: 39A12 39A10 34C30 43A80 22E30 PDFBibTeX XMLCite \textit{D. Levi} et al., J. Phys. A, Math. Gen. 30, No. 2, 633--649 (1997; Zbl 0956.39013) Full Text: DOI
Spiridonov, Vyacheslav; Vinet, Luc; Zhedanov, Alexei Spectral transformations, self-similar reductions and orthogonal polynomials. (English) Zbl 0926.39006 J. Phys. A, Math. Gen. 30, No. 21, 7621-7637 (1997). MSC: 39A12 42C05 33D45 PDFBibTeX XMLCite \textit{V. Spiridonov} et al., J. Phys. A, Math. Gen. 30, No. 21, 7621--7637 (1997; Zbl 0926.39006) Full Text: DOI
Spiridonov, Vyacheslav; Vinet, Luc; Zhedanov, Alexei Discrete Schrödinger equation, Darboux transformations, and orthogonal polynomials. (English) Zbl 0859.33016 Levi, Decio (ed.) et al., Symmetries and integrability of difference equations. Papers from the workshop, May 22–29, 1994, Estérel, Canada. Providence, RI: American Mathematical Society. CRM Proc. Lect. Notes. 9, 363-369 (1996). Reviewer: H.Kriete (Göttingen) MSC: 33D45 39A10 PDFBibTeX XMLCite \textit{V. Spiridonov} et al., in: Symmetries and integrability of difference equations. Papers from the workshop, May 22--29, 1994, Estérel, Canada. Providence, RI: American Mathematical Society. 363--369 (1996; Zbl 0859.33016)
Levi, Decio (ed.); Vinet, Luc (ed.); Winternitz, Pavel (ed.) Symmetries and integrability of difference equations. Papers from the workshop, May 22–29, 1994, Estérel, Canada. (English) Zbl 0852.00027 CRM Proceedings & Lecture Notes. 9. Providence, RI: American Mathematical Society (AMS). xii, 388 p. (1996). MSC: 00B25 39-06 PDFBibTeX XMLCite \textit{D. Levi} (ed.) et al., Symmetries and integrability of difference equations. Papers from the workshop, May 22--29, 1994, Estérel, Canada. Providence, RI: American Mathematical Society (1996; Zbl 0852.00027)
Floreanini, Roberto; Negro, Javier; Nieto, Luis Miguel; Vinet, Luc Symmetries of the heat equation on the lattice. (English) Zbl 0851.39007 Lett. Math. Phys. 36, No. 4, 351-355 (1996). Reviewer: E.Trofimtchouk (Kiev) MSC: 39A12 81T25 39A10 35K05 PDFBibTeX XMLCite \textit{R. Floreanini} et al., Lett. Math. Phys. 36, No. 4, 351--355 (1996; Zbl 0851.39007) Full Text: DOI
Levi, D.; Vinet, L.; Winternitz, P. Symmetries of discrete physical systems. (English) Zbl 0948.37501 Atakishiyev, N. M. (ed.) et al., Proceedings of the IV Wigner symposium, Guadalajara, Mexico, August 7-11, 1995. Singapore: World Scientific. 383-391 (1996). MSC: 37L20 35A30 35R10 39A99 PDFBibTeX XMLCite \textit{D. Levi} et al., in: Proceedings of the IV Wigner symposium, Guadalajara, Mexico, August 7--11, 1995. Singapore: World Scientific. 383--391 (1996; Zbl 0948.37501)
Floreanini, Roberto; Vinet, Luc Lie symmetries of finite-difference equations. (English) Zbl 0859.39008 J. Math. Phys. 36, No. 12, 7024-7042 (1995). Reviewer: L.Berg (Rostock) MSC: 39A12 39A10 35J05 35K05 35L05 33C45 PDFBibTeX XMLCite \textit{R. Floreanini} and \textit{L. Vinet}, J. Math. Phys. 36, No. 12, 7024--7042 (1995; Zbl 0859.39008) Full Text: DOI
Floreanini, Roberto; Vinet, Luc Quantum symmetries of \(q\)-difference equations. (English) Zbl 0859.39007 J. Math. Phys. 36, No. 6, 3134-3156 (1995). Reviewer: E.Thandapani (Salem) MSC: 39A12 39A70 81R50 17B37 PDFBibTeX XMLCite \textit{R. Floreanini} and \textit{L. Vinet}, J. Math. Phys. 36, No. 6, 3134--3156 (1995; Zbl 0859.39007) Full Text: DOI
Floreanini, Roberto; Vinet, Luc Symmetries of \(q\)-deformed heat equations. (English) Zbl 0942.33500 Doebner, H.-D. (ed.) et al., Nonlinear, deformed and irreversible quantum systems. Proceedings of the international symposium on mathematical physics, Technical University Clausthal, Germany, August 15-19, 1994. Singapore: World Scientific. 385-400 (1995). MSC: 33D90 33D80 39A12 58J35 81R50 PDFBibTeX XMLCite \textit{R. Floreanini} and \textit{L. Vinet}, in: Nonlinear, deformed and irreversible quantum systems. Proceedings of the international symposium on mathematical physics, Technical University Clausthal, Germany, August 15--19, 1994. Singapore: World Scientific. 385--400 (1995; Zbl 0942.33500)
Floreanini, Roberto; Vinet, Luc Symmetries of the \(q\)-difference heat equations and discrete \(q\)-Hermite polynomials. (English) Zbl 0899.39001 Arima, A. (ed.) et al., Yamada conference XL. Proceedings of the XXth international colloquium on group theoretical methods in physics, Toyonaka, Japan, July 4-9, 1994. Singapore: World Scientific. 491-494 (1995). MSC: 39A10 33D90 PDFBibTeX XMLCite \textit{R. Floreanini} and \textit{L. Vinet}, in: Yamada conference XL. Proceedings of the XXth international colloquium on group theoretical methods in physics, Toyonaka, Japan, July 4-9, 1994. Singapore: World Scientific. 491--494 (1995; Zbl 0899.39001)
Floreanini, Roberto; Vinet, Luc Symmetries of the \(q\)-difference heat equation. (English) Zbl 0805.39008 Lett. Math. Phys. 32, No. 1, 37-44 (1994). Reviewer: E.Trofimtchouk (Kiev) MSC: 39A10 81R99 33D45 33D80 PDFBibTeX XMLCite \textit{R. Floreanini} and \textit{L. Vinet}, Lett. Math. Phys. 32, No. 1, 37--44 (1994; Zbl 0805.39008) Full Text: DOI
Spiridonov, Vyacheslav; Vinet, Luc; Zhedanov, Alexei Difference Schrödinger operators with linear and exponential discrete spectra. (English) Zbl 0790.33017 Lett. Math. Phys. 29, No. 1, 63-73 (1993). Reviewer: A.K.Agarwal (Grambling) MSC: 33D70 39A70 17B37 81R50 PDFBibTeX XMLCite \textit{V. Spiridonov} et al., Lett. Math. Phys. 29, No. 1, 63--73 (1993; Zbl 0790.33017) Full Text: DOI