ON COMPOUND BOUNDARY PROBLEM OF ANALYTIC FUNCTION WITH SHIFTS
Huang Haiyang
Let D be a m+n+1 connected domain bounded by closed Ljapunov curves L= Li,T=,and in the interior of D there are some disjoint closed Ljapunov curves l=.The domain D is partitioned by l,f into two parts:D~+ and D~. In this paper,the Haseman,Hasemantype,Carleman,Carlemantype compound boundary problem is considered: Find a piecewise analytic ruction Φ(z)in D(i.e,Φ(z)is analytic in D~+,D~ and continuous to f,l on each side of them)such that Φ~+[η(t)]=G(t)Φ~(t)+g(t),for t∈f, Φ~++[γ(t)]=G(t)+g(t),for t∈l, simultaneously Φ(z)be continuous to L,Γfrom the interior of D and satisfy Φ+[β(t)]=G(t)~+(t)+g(t),for t∈Γ, Φ~+[α(t)]=G(t),for t∈L, where G(t),g(t)EH and G(t)(?)0,for t∈lUf, G(t)G[β(t)]=1,G(t)g[β(t)]+g(t)=0,for t∈Γ, G(t)G[α(t)=1,G(t)g[α(t)]+g(t)=0,for t∈L, γ(t),β(t)are reverse shifts on l,Γ respectively and η(t),α(t)are positive shifts on f,L respectively,α[α(t)]≡t,β[β(t)]≡t,α'(t)0,β'(t)0,η'(t) 0,γ~'(t)0 and α'(t),β'(t),η'(t),γ'(t)∈H. This problem may be solved by conformal mapping and elimination: first this problem is transformed into R,Ctype problem by conformal mappi ng,then R,Ctype problem is reduced to Ctype problem by elinination,and finally the solvability theorem of thisproblem according to the solvability theorem of Ctype problem is obtained.


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