Geodesic
Subharmonic envelopes for functions on domains
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 29 (2023) no. 3, pp. 64-71 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {Subharmonic envelopes for functions on domains},
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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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