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The Riemann boundary value problem in the space \(L_ p(\Gamma,\rho)\) with almost periodic discontinuities at its coefficients. (Russian) Zbl 0577.45004

The authors consider the Riemann boundary value problem in the space \(L_ p(\Gamma,\rho)\) on a simple closed Lyapunov contour (1) \(\phi^+(t)-a(t)\phi^-(t)=f(t)\), \(t\in \Gamma\), where \(a(t)=\tilde a(t)\prod^{w}_{k=1}\exp [a_ k(t-t_ k)^{-1}]\), \(t_ k\in \Gamma\), \(a_ k\in {\mathbb{C}}\), \(\tilde a(\)t)\(\in L_{\infty}(\Gamma)\) admitting a generalized factorization. The structure of ker and coker of problem (1) is investigated and an explicit construction of the inverse operator is given.
Reviewer: V.S.Rabinovič

MSC:

45E05 Integral equations with kernels of Cauchy type
30E25 Boundary value problems in the complex plane
35Q15 Riemann-Hilbert problems in context of PDEs
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