Factorization of the Heun’s differential operator. (English) Zbl 1035.34100
The author studies the factorization over \(\mathbb{C}[z]\) of the differential operator
\[
H\equiv P_{3}D^{2}+P_{2}D+P_{1},
\]
where
\[
D\equiv\frac{d}{dz}, P_{i}\in \mathbb{C}[z],
\]
and \(\text{deg\,}P_{i}=i\) (Heun’s operator). The problem is completely investigated by simple methods. However, the author does not solve the problem of reducibility of Heun’s operator over \(\mathbb{C}(z)\). For the algebraic point of view of that problem see J. Kovacic [Proc. Am. Math. Soc. 34, 25–29 (1972; Zbl 0236.12106)].
Reviewer: Nikolay Vasilye Grigorenko (Kyïv)
Citations:
Zbl 0236.12106References:
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