Geodesic
Subharmonic envelopes for functions on domains
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 29 (2023) no. 3, pp. 64-71

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One of the most common problems in various fields of real and complex analysis is the questions of the existence and construction for a given function of an envelope from below or from above of a function from a special class $H$. We consider a case when $H$ is the convex cone of all subharmonic functions on the domain $D$ of a finite-dimensional Euclidean space over the field of real numbers. For a pair of subharmonic functions $u$ and $M$ from this convex cone $H$, dual necessary and sufficient conditions are established under which there is a subharmonic function $h\not\equiv -\infty$, “dampening the growth” of the function $u$ in the sense that the values of the sum of $u+h$ at each point of $D$ is not greater than the value of the function $M$ at the same point. These results are supposed to be applied in the future to questions of non-triviality of weight classes of holomorphic functions, to the description of zero sets and uniqueness sets for such classes, to approximation problems of the function theory, etc.
Keywords: subharmonic function, lower envelope, ordered space, vector lattice, projective limit, linear balayage, Jensen measure, holomorphic function. 
B. N. Khabibullin. Subharmonic envelopes for functions on domains. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 29 (2023) no. 3, pp. 64-71. http://geodesic.mathdoc.fr/item/VSGU_2023_29_3_a7/
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