推关复 邻域内 函给 取。 1≡U1 z∈G1∩G 证得定拓法区(63)我延互 2+p(2)-+q(2)1= g(z)在G2内延析因或U1拓法区(6.3)在程域G1内我延, 程域G1∩G2内,定析性法区 p( )+g(2) dz 而在此,程域内,1(2)≡i1(z), d22+p(e dur d 2i q(2)1=0,z∈G1∩G2 即g(2)≡0,z∈G1∩G2根据延析也我唯一性,立即证得 g(2)≡0 亦即1在G2内析性法区 +p(x) 例6.5全m1依2都拓法区(6.3)我两个线性无a延,且均在程域G1内延析,由 i1依2分别拓矶1依砌2在程域G2内我延析解是,即在z∈G1∩G2中 三1,2≡u2 t1依2定线性无 若例64知,画侬高定拓法区(在C2肉)我延因或m2依线性无 U1 2 ≠0,z∈G1 全 W1 70 g(2)在G2内延析,若于在z∈G1∩G2中 别 g(2)≠0,z∈G1∩G2定然根据延析也我唯一性,就证得 g(2)≠0,z∈G2 所以,1依2(在G2内)定线性无 程互§6.2 ✡☛✞➦üý þ☞✏ ✒ 6 ✓ w1 ≡ we1, z ∈ G1 T G2, (6.4) ◗ ➽ ➾➍ we1 ❘▼❋● (6.3) ❍▲❑ ❙ ❖ d 2we1 dz 2 + p(z) dwe1 dz + q(z)we1 = g(z), g(z) ❹ G2 ➱▲❱❑➤ ❊ w1 ▼❋● (6.3) ❹●Ü G1 ➱❍▲❯❚ ❹❯●Ü G1 T G2 ➱❯❘❱❲❋● d 2w1 dz 2 + p(z) dw1 dz + q(z)w1 = 0. ✰❹ ➥ ❯●Ü ➱❯ w1(z) ≡ we1(z) ❯ ❚ d 2we1 dz 2 + p(z) dwe1 dz + q(z)we1 = 0, z ∈ G1 T G2, ➩ g(z) ≡ 0, z ∈ G1 T G2 ❑ ×Ø▲❱☞❏❍Ó➁❲❯❳➩➽ú g(z) ≡ 0, z ∈ G2, ❨ ➩ we1 ❹ G2 ➱❱❲❋● d 2we1 dz 2 + p(z) dwe1 dz + q(z)we1 = 0. ➅ 6.5 ❖ w1 ❈ w2 → ▼ ❋ ● (6.3) ❍ ➌ ➂ ✔ ❲ ➙ ☛ ▲ ❯Õ ò ❹ ● Ü G1 ➱▲ ❱ ❑P we1 ❈ we2 ❮❚▼ w1 ❈ w2 ❹●Ü G2 ➱❍▲❱▲▼❯➩❹ z ∈ G1 T G2 ❽ w1 ≡ we1, w2 ≡ we2. ◗ ➽➍ we1 ❈ we2 ❘✔❲ ➙ ☛❑ ❙ P✹ 6.4 ❩❯ we1 ❈ we2 ❘▼❋● (❹ G2 ➱) ❍▲❑➤ ❊ w1 ❈ w2 ✔❲ ➙ ☛❯ ∆[w1, w2] ≡      w1 w2 w 0 1 w 0 2      6= 0, z ∈ G1. ❖ ∆[we1, we2] ≡      we1 we2 we 0 1 we 0 2      = g(z), g(z) ❹ G2 ➱▲❱❑P✮❹ z ∈ G1 T G2 ❽❯ w1 ≡ we1, w2 ≡ we2, ❚ g(z) 6= 0, z ∈ G1 T G2 ❑❘ á×Ø▲❱☞❏❍Ó➁❲❯î➽ú g(z) 6= 0, z ∈ G2. ➎➏❯ we1 ❈ we2(❹ G2 ➱) ❘✔❲ ➙ ☛❑