Abstract:
Given a continuous complex-valued function a and nonnegative functions ρ1 and ρ2 on a two-dimensional smooth connected closed surface such that |a|=ρ1ρ2 and the functions ρ1 and ρ2 have no common zeros, it is required to find complex-valued continuous functions a1 and a2 satisfying the conditions a1a2=a and |aj|=ρj. Necessary and sufficient solvability conditions for this problem are given.
Citation:
A. P. Soldatov, “A Factorization Problem on a Smooth Two-Dimensional Surface”, Mat. Zametki, 108:2 (2020), 285–290; Math. Notes, 108:2 (2020), 272–276
This publication is cited in the following 1 articles:
Pavel Shabalin, Rafael Faizov, E. Vdovin, “Hilbert boundary value problem for generalized analytic functions with a singular line”, E3S Web Conf., 274 (2021), 11003