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
