Problems Of Function Theory And Their Application To Mathematical Physics N I Muskhelishvili - Singular Integral Equations Boundary

[ (a(t) + b(t)) \Phi^+(t) - (a(t) - b(t)) \Phi^-(t) = f(t). ]

with given Hölder-continuous ( G(t) \neq 0 ) and ( g(t) ). The of the problem is [ (a(t) + b(t)) \Phi^+(t) - (a(t) - b(t)) \Phi^-(t) = f(t)

[ \Phi^\pm(t_0) = \pm \frac12 \phi(t_0) + \frac12\pi i , \textP.V. \int_\Gamma \frac\phi(t)t-t_0 , dt, ] \textP.V. \int_\Gamma \frac\phi(t)t-t_0

[ \Phi(z) = \frac12\pi i \int_\Gamma \frac\phi(\tau)\tau-z , d\tau, ] [ (a(t) + b(t)) \Phi^+(t) - (a(t) - b(t)) \Phi^-(t) = f(t)