Abstract. 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), t ∈ 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.
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