Completeness of systems of functions, quasianalyticity and subharmonic majorants
Completeness of systems of functions, quasianalyticity and subharmonic majorants
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函数系统的完备性、准解析性和次谐波主调
DOI：
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发表时间：
1993
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通讯作者：
B. Y. Levin
中科院分区：
文献类型：
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作者：
B. Y. Levin
本文研究了某些常见的整函数系在σ-空间(例如，在C(E)中，E是R的闭子集)中的完备性问题(例如，所有阶不超过给定个数Φ的整函数系的完备性)。对偶问题是关于函数类的拟渐近性的问题，其傅立叶变换被支承在一个薄集合上。利用位势理论技巧，借助于上半平面到特殊梳状区域的共形映射的研究，解决了后一类问题。
In the paper one investigates completeness questions for certain frequently encountered systems of entire functions (for example, the completeness of the system of all entire functions of order not exceeding a given number σ) in Φ-spaces (for example, in C(E), E being a closed subset of R). Dual problems are the problems regarding the quasianatyticity of classes of functions, having Fourier transforms supported on a thin set. These latter problems are solved with the use of potential theory technique and with the aid of the investigation of conformal mappings of the upper half-plane onto special comb-like domains.