| Lu JIANKE.[J].数学年刊A辑,1980,1(2):289~298 |
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| ON DOUBLY-PERIODIC RIEMANNIAN BOUNDARYVALUE PROBLEMS ALONG OPEN ARCS |
| Received:October 03, 1979 |
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| 英文摘要: |
| In this paper, we consider the doubly-periodio Riemannian boundary value pro-
blems (1.1) along a set L of smooth open arcs, any two of which are congruent to each
other with respect to the two periods. In (1.1), G(t) ≠0 and g(t) are given functions
on L, continuons in Holder and sense doubly-periodio, and \[{\Phi ^ \pm }(t)\] are the boundary
values of the unknown doubly-periodio analytic function \[\Phi (z)\] along the different
sides of L. Such problems are solved effectively so that both the solutions and the
conditions of solvability are obtained in explicit forms. The results are then applied
to solving certain classes of singular integral equations like (4.1) and (4,5) with
kernels involving Weierstrass \[\xi \] functions. The case in which the two ends of each
arc are congruent is also considered and similarly solved. |
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