Abstract
Symmetric representations of holomorphic functions
Highlights
Q ∈ N; G is an open set in Cn; π : G → Cq is a holomorphic mapping
A set g ⊆ G is called π-symmetric, if there exists a set V in Cq such that g = π−1(V )
The class of π-symmetric functions is needed to consider some representations of holomorphic on complex domain functions
Summary
Π : G → Cq is a holomorphic mapping. A set g ⊆ G is called π-symmetric, if there exists a set V in Cq such that g = π−1(V ). The class of π-symmetric functions is needed to consider some representations of holomorphic on complex domain functions. Q−1 p=1 zpup(z), where up ∈ Oπ(G) [1] Such presentation is called a symmetric representation of the analytic function [2]. Note that the concept of symmetric representation of an analytic function plays a key role in some questions of complex analysis. For example it is used in spectral synthesis (see [3–6]). Zp ∈ λis called an alphabetized list of the set λ, if j < k ⇔ ∃ m ∈ [1, n) such that j1 = k1, . We have: i) any two adjacent submatrices have the same columns except exactly one called marked ; ii) any marked column consists of equal elements. The elements of m-th columns are equal to zj(m−1) and zj(m), respectively
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