Some results on the invertibility of Toeplitz plus Hankel operators

The paper deals with the invertibility of Toeplitz plus Hankel operators T(a)+H(b) acting on classical Hardy spaces on the unit circle T. It is supposed that the generating functions a and b satisfy the condition a(t)a(1/t)=b(t)b(1/t). Special attention is paid to the case of piecewise continuous generating functions. In some cases the dimensions of null spaces of the operator $T(a)+H(b)$ and its adjoint are described.