Singular Integral Equations Boundary Problems Of Function Theory And Their Application To Mathematical Physics N I Muskhelishvili May 2026

defines two analytic functions: ( \Phi^+(z) ) inside, ( \Phi^-(z) ) outside. Their boundary values on ( \Gamma ) satisfy

[ \Phi^+(t) = G(t) , \Phi^-(t) + g(t), ] defines two analytic functions: ( \Phi^+(z) ) inside,

[ \Phi(z) = \frac12\pi i \int_\Gamma \frac\phi(t)t-z , dt ] \Phi^-(t) + g(t)

with ( a(t), b(t) ) Hölder continuous. The key is to set dt ] with ( a(t)