Commuting Krichever-Novikov differential operators with polynomial coefficients.

Under study are some commuting rank 2 differential operators with polynomial coefficients. We prove that, for every spectral curve of the form w = z + c z 2+ c z+ c with arbitrary coefficients c , there exist commuting nonselfadjoint operators of orders 4 and 6 with polynomial coefficients of arbitrary degree. [ABSTRACT FROM AUTHOR]