Abstract
AbstractIt is well known that the finite HILBERT transform T is a NOETHER (FREDHOLM) operator when considered as a map from ℒp into itself if 1 < p < 2 or 2 < p < ∞. When p = 2, the map T is not a NOETHER operator. We present two theorems which characterize the range of T in ℒ2 and, as immediate consequences, give simple expressions for its inverse.
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