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CONVERSE OF BURCHNALL-CHAUNDY THEOREM AND APPLICATIONS FOR THE FIRST WEYL ALGEBRA
Keywords:
first Weyl algebra, commuting operators.DOI:
https://doi.org/10.17654/0972087124006Abstract
In the context of the first Weyl algebra, we prove the converse of Burchnall-Chaundy theorem and show some of its applications.
Received: January 14, 2024
Accepted: February 29, 2024
References
J. Dixmier, Sur les algèbres de Weyl, Bull. Soc. Math. France 96 (1968), 209-242.
V. Tulovsky, On the construction of commuting operators in the first Weyl algebra, I, Far East J. Math. Sci. (FJMS) 139 (2022), 39-57.
V. Tulovsky, Some applications of Weyl calculus to Burchnall-Chaundy theory, II, Far East J. Math. Sci. (FJMS) 138 (2022), 45-60.
V. Tulovsky, Some applications of Weyl calculus to Burchnall-Chaundy theory, I, Far East J. Math. Sci. (FJMS) 117(2) (2019), 113-118.
J. L. Burchnall and T. W. Chaundy, Commutative ordinary differential operators, Proc. R. Soc. Lond. A 118 (1928), 557-583.
S. Amitsur, Commutative linear differential operators, Pacific J. Math. 8(1) (1958), 1-10.
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