Fredholm operator

(redirected from Fredholm index)

Fredholm operator

[′fred‚hōm ‚äp·ə‚rād·ər]
(mathematics)
A linear operator between Banach spaces which has closed range, and both the Fredholm operator and its adjoint have finite dimensional null space.
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[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]).