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SOME APPLICATIONS OF WEYL CALCULUS TO BURCHNALL-CHAUNDY THEORY, IV
Keywords:
Burchnall-Chaundy theory, Weyl algebraDOI:
https://doi.org/10.17654/0972087126018Abstract
Suppose that $A, B$ are differential operators with polynomial coefficients and they commute. Then there is a polynomial $f(\lambda, \mu)$ such that $f(A, B)=0$. The set of all such polynomials is a principal ideal $J$. In this paper, we develop an algorithm for finding the generator of $J$ in some particular cases.
Received: August 10, 2025
Accepted: September 15, 2025
References
[1] J. L. Burchnall and T. W. Chaundy, Commutative ordinary differential operators, Proc. R. Soc. Lond. A 118 (1928), 557-583.
[2] V. Tulovsky, Some applications of Weyl calculus to Burchnall-Chaundy theory, I, Far East J. Math. Sci. (FJMS) 117(2) (2019), 113-118.
[3] V. Tulovsky, Some applications of Weyl calculus to Burchnall-Chaundy theory, II, Far East J. Math. Sci. (FJMS) 138 (2022), 45-60.
[4] V. Tulovsky, Some applications of Weyl calculus to Burchnall-Chaundy theory, III, Far East J. Math. Sci. (FJMS) 142(1) (2025), 9-24.
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