Abstract
The problem of finding two rational, linearly related functions with poles in the half-planes is considered. A new approach to this theory is proposed. The problem with factorable rational coefficients is formulated and solved. The method is based on the theory that is derived from previous research by the second author. The result is used for the corresponding abstract equations in the ring, with a special factorization pair of subrings. The formulas of solutions and illustrative examples are given. The procedure does not involve Fourier integral, Cauchy integral theory, or the Hölder function.
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