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Generalized and ultra Markushevihc problems for generalized analytic functions

Is not equal to zero. G (t5G: (£) can be ultra-flat extension to analytic functions G (z5, and meet ImG (z) G (= j 10. Can get: Lemma 2 Let G (z) for ultra-analytic functions, namely, 96 (z) = 0, if ImG (z) G (Z ~ 5 = 0 and (:) for the complex equations (195 in the D + U, 9 a solution, then (z) = W (z) + G (:) W A (5 form complex equations (19) in D, negligent use of the method given in the text _21, see also the corresponding notation in [21, problem (2o5 solution can be transformed into two equivalent equations ie Re [(r)] is equivalent to the equations of a Im: (215L1, 10, a cylinder a-D0Lll HL, +1-1. one thousand one hundred and eleven '8 Fuzhou University (Natural Science) 27 Volume I: + is (2U solution for (21) corresponding homogeneous equation of the ship, yo jack a (. din) * non-homogeneous equation (21) with special solutions and Re) a))] m) equivalent equations, 1lReW [(f) = y a (zeD) (f ∈) which: the main one by one (k-I + B1wk_f ten), | 2 '..., r - l, a. solving system of equations (21) j take j (z) a 』Im} fu, too: I) when ≥ one, =』 expRe ~ so fu + Σct: / [expi (z)] where c is a complex constant, which satisfies the condition c2 a = a c, (= 0,[link widoczny dla zalogowanych],1, ..., n) .2) When n <0, when and only if the following solvability condition: j c expRei () · r one. d one. (a ., 1, ..., one by one 1) 1 and the only one by one relentless jexpRe ~) ar so solving system of equations (22), was W a (z) = Σ {exp [q ~ (z) A zt (: )] 2 Ⅱ f-Re (t) t + zdt ~ (z )+(:) expix (z)) {_1cxp_I) 1 』expRe [~ k - Zk] to] df + id0exp [q ~ (a) a z (a )]+()} d (22 ) (23) (24) (25) (26) (27) t 2 Chen Jinyu: generalized and generalized analytic functions Markushevich over the issue. 9. that the form 0 ... 10 ... ... 0 ... ... 0 ... 0 ● ... ● ● l0 matrix ,(=)= m (z) exp ~ o (z) to (21) of the corresponding homogeneous equation (=) to equation (21) the particular solution, z (z) a go 』Im Fu, d is a real constant, F is the r surface may theorem. Theorem 2 Let G (r) a G2 (r) the unit circle to be Extended to analytic functions within a super-G), and meet ImG (z) G) = 0, if n ≥ 0, then the Boundary Problems (19) must be solvable, its solution is given by (26), (27) decided that when <0 if and only if (24) is satisfied, the problem has a unique a solution. thank Professor Wang Chuanrong article by the noted instructor 0 guidance, to express heartfelt thanks.