Let u and M are two non-trivial subharmonic functions in a domain D in the complex plane. We investigate two related but different problems. The first is to find the conditions on the Riesz measures of functions u and M respectively under which there exists a non-trivial subharmonic function h on D such that u+h< M. The second is the same question, but for a harmonic function h on D. The answers to these questions are given in terms of the special affine balayage of measures introduced in our recent previous works. Applications of this technique concern the description of distribution of zeros for holomorphic functions f on the domain D satisfying the restriction |f|< exp M.
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[v1] 2019-08-25 14:34:25
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