2025/05/11 by Muhamed Borogovac, Borogovac, Muhamed · 1 citation
Computer Science · Mathematics · #(2020) 47A56 30D30 34M04 47B50 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2505.06812
openalex publication_date 2025/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A practical method is presented for determining root and pole cancellation functions of a matrix function Q(z) meromorphic on the extended complex plane ℂ:=ℂ ∪ \ ∞ \. This method is applied to solve a nonlinear system of n∈ ℕ differential equations of order l∈ ℕ with n unknown functions ui( t ), where i=1, \mathellipsis , n . For a function Q∈ Nκ(H) , κ∈ ℕ ∪ \lbrace 0 \rbrace, posesing a pole at infinity of order m ∈ ℕ, the following factorization is establish Q(z)=(z-β)mQ(z), z∈ D(Q), where β∈ ℝ is a regular point of Q, and Q∈ Nκ'(H) is holomotphic at ∞. Unlike the Krein-Langer representation of Q, which involves a linear relation A, this representation employs a bounded operator A in the Krein-Langer representation of Q. The operator A and the relation A have identical spectra, except at β and ∞. We demonstrate how to obtain this representation for a given meromorphic function Q∈ Nκn × n using the root functions developed in this work.