Abstract:
Self-adjoint commuting differential operators with polynomial coefficients are considered. These operators form a commutative subalgebra of the first Weyl algebra. New examples of commuting differential operators of rank 2 are found.
Keywords:
differential operator, first Weyl algebra, Krichever–Novikov equation, Dixmier hypothesis, nonlinear equation,
operator of nontrivial rank.
This publication is cited in the following 13 articles:
J. Guo, A. Zheglov, “On Some Questions around Berest's Conjecture”, Math. Notes, 116:2 (2024), 238–251
A. F. Gundareva, “Commuting elements in the first Weyl algebra over $\mathbb{Q}$”, Siberian Math. J., 63:5 (2022), 883–893
Leonid Makar-Limanov, “Centralizers of Rank One in the First Weyl Algebra”, SIGMA, 17 (2021), 052, 13 pp.
V. Oganesyan, “Matrix commuting differential operators of rank 2 and arbitrary genus”, Int. Math. Res. Notices, 2019, no. 3, 834–851
Emma Previato, Sonia L. Rueda, Maria-Angeles Zurro, “Commuting Ordinary Differential Operators and the Dixmier Test”, SIGMA, 15 (2019), 101, 23 pp.
V. S. Oganesyan, “Commuting Differential Operators of Rank 2 with Rational Coefficients”, Funct. Anal. Appl., 52:3 (2018), 203–213
V. S. Oganesyan, “Alternative proof of Mironov's results on commuting self-adjoint operators of rank 2”, Siberian Math. J., 59:1 (2018), 102–106
V. S. Oganesyan, “The AKNS hierarchy and finite-gap Schrödinger potentials”, Theoret. and Math. Phys., 196:1 (2018), 983–995
D. A. Pogorelov, A. B. Zheglov, “An algorithm for construction of commuting ordinary differential operators by geometric data”, Lobachevskii J. Math., 38:6 (2017), 1075–1092
V. N. Davletshina, A. E. Mironov, “On commuting ordinary differential operators with polynomial coefficients corresponding to spectral curves of genus two”, Bull. Korean. Math. Soc., 54:5 (2017), 1669–1675
V. Oganesyan, “Explicit characterization of some commuting differential operators of rank 2”, Int. Math. Res. Not. IMRN, 2017, no. 6, 1623–1640
V. S. Oganesyan, “On operators of the form $\partial_x^4+u(x)$ from a pair of commuting differential operators of rank 2 and genus $g$”, Russian Math. Surveys, 71:3 (2016), 591–593
A. E. Mironov, “Self-adjoint commuting differential operators of rank two”, Russian Math. Surveys, 71:4 (2016), 751–779
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