Exact solution of a simple hypersingular integral equation (Q1195352)

The author considers in a Hölder type space the following linear hypersingular integral equation \(Hf=v\), where \[ \begin{multlined} (Hf)(x)=\int^ 1_{-1}(x-t)^{-2}f(t)dt:=\\ =\lim_{\varepsilon\to 0}\left\{\int^{x-\varepsilon}_{-1}(x-t)^{-2}f(t)dt+\int^ 1_{x+\varepsilon} (x-t)^{-2}f(t)dt+-2\varepsilon^{- 1}f(x)\right\},\quad x\in(-1,1).\end{multlined} \] The general solution of this equation and some remarks on closed contours and Chebyshev polynomials are given.