Equiconvergence of expansions in eigenfunctions of integral operators with kernels that can have discontinuities on the diagonals

Simple conditions are found ensuring the equiconvergence of the Fourier expansion of a function $f(x)$ in $L[0,1]$ in the eigenfunctions and the associated functions of an integral operator
$$ Af=\int_0^{1-x}A(1-x,t)f(t)\,dt+\alpha\int_0^xA(x,t)f(t)\,dt $$
and the expansions of $f(x)$ and $f(1-x)$ in the standard trigonometric system.