We construct differential operators
Lg(z), Kg(z), Nf¯(z), Mf¯z) which map arbitrary functions holomorphic in a simply connected domain
D of the plane
z=x+iy into regular solutions of the equation
Wz[`(z)] + A(z,[`(z)])W[`(z)] + B(z,[`(z)])W = 0W_{z\bar z} + A(z,\bar z)W_{\bar z} + B(z,\bar z)W = 0
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and present examples of the application of these differential operators to the solution of fundamental boundary-value problems in mathematical physics.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 12, pp. 1587–1592, December, 1995.