摘要
本文用矩阵函数带位移分解方法讨论多个未知函数的Cazleman内问题(I),得到下面三个结果:1)问题(Ⅰ)的齐次问题与其相联问题(Ⅱ)线性无关解个数有限;2)问题(Ⅰ)正规可解;3)问题(Ⅰ)的指标1按公式I=(p+q-k)/2计算,式中p,q分别是数值矩阵G(t_1)和G(t_2)的正特征值个数,t_1,t_2是反位移a(t)的两个不动点,而k=Ind_(Γ)(det(C(t))).
It is discussed that the Carlemanian boundary value problem for several unknown functions by the means of factorization with shift of matrix functions. The following results are got: The problem (I) is a Noetherian problem and the index of problem is given by the following formula:I=1/2(p+q-k), where p, q are the numbers of positive eigenvalue of numerical matrices G(t_1) and G(t_2), respectively; t_1 and t_2 are the fixed points of the negative shift a(t); and k=Ind(det(G(t))).
出处
《北京师范大学学报（自然科学版）》
CAS
1985年第4期1-9,共9页
Journal of Beijing Normal University(Natural Science)
