Spectral Synthesis in a Complex Domain for a Differential Operator With Constant Coefficients. I: A Duality Theorem

Symmetric representations of holomorphic functions

“…In particular, any π-layer equals to the respectiveπ-layer. Let π be a special analytic covering, z ∈ G * and π(z) = λ = (λ (1) , . .…”

“…is a compact set in g (i) . It follows from theorem 1 that the function F is analytic on a set G = (g (1) ) p(1) × . .…”

“…G is an open π-symmetric set in C. Note the following theorem: Any u ∈ O(G) has the unique representation of the form u(z) = q−1 p=1 z p u p (z), where u p ∈ O π (G) [1]. Such presentation is called a symmetric representation of the analytic function [2].…”

“…, p(1), are the last column of Z k−1 and the first column of Z k . Elements of these columns are equal to elements of z (1) k−3 and z (1) k , respectively. Then add columns to Z 4 , .…”