Contribution to the General Linear Conjugation Problem for A Piecewise Analytic Vector

Сибирский математический журнал

S. N. Kiyasov¹ 

[1] Kazan (Volga Region) Federal University

关键词: matrix function;    linear conjugation problem;    factorization;   

DOI  :  10.1134/S003744661802012X

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

Establishing an analogy between the theories of Riemann–Hilbert vector problem and linear ODEs, for the n-dimensional homogeneous linear conjugation problem on a simple smooth closed contour Γ partitioning the complex plane into two domains D+ and D− we show that if we know n−1 particular solutions such that the determinant of the size n−1 matrix of their components omitting those with index k is nonvanishing on D+ ∪ Γ and the determinant of the matrix of their components omitting those with index j is nonvanishing on Γ ∪ D− {∞}, where \(k,j = \overline {1,n} \), then the canonical system of solutions to the linear conjugation problem can be constructed in closed form.

【 授权许可】

CC BY