[14, 27, 29] and the references therein), integral equations governed by Toeplitz plus Hankel operators acting between Lebesgue spaces on the half-line have obtained significant progress only recently as it concerns their invertibility and Fredholm property characterizations, as well as Fredholm index
theory, for several specific classes of kernel functions; cf.
The Fredholm index
of an operator T in F is the integer ind(T) = dimN(T) - dimN([T.sup.*]).
In the general case, we first compute the Fredholm index
of P, and then we use this computation to obtain a decomposition u = [u.sub.reg] + [sigma] of the solution of u of (1.1) into a function with good decay at the vertices and a function that is locally constant near the vertices.
If L is a Fredholm mapping, its Fredholm index
is the integral IndL = dim kerL--codimImL.
In this case, the operator is one-sided invertible and its Fredholm index
is equal to ind (aI + bS) = -wind c (x, [lambda]).