2018/12/22 by Б. Н. Хабибуллин, Khabibullin, B. N., A. P. Rozit +3 · 1 citation
Mathematics · #31C05 #31C10 #32A10 #32A60 #46A40 #46E05 #Advanced Banach Space Theory #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1812.11058
openalex publication_date 2018/12/22 · openalex created_date 2019/01/11 · openalex updated_date 2026/07/28
Chapter 1 deals with the problem of the existence of an upper/lower envelope from a convex cone or, more generally, a convex set for functions on the projective limit of vector lattices with values in the completion of the Kantorovich space or on the extended real line. Vector, ordinal and topological dual interpretations of the existence conditions of such envelope and the method of its construction are given. Chapter 2 presents applications to the existence of a nontrivial (pluri)subharmonic and/or (pluri) harmonic minorant for functions in domains from finite-dimensional real or complex space. General approaches to the problems of nontriviality of weight classes of holomorphic functions, to the description of zero (sub)sets for such classes of holomorphic functions, to the problem of representation of a meromorphic function as a ratio holomorphic functions from a given weight class are indicated.