Abstract
We consider infinite-dimensional generalized Hilbert matrices of the form H i , j = d i d j x i + x j , where di are nonnegative weights and xi are pairwise distinct positive numbers. We state sufficient and, for monotonically rearrangeable xi , also necessary conditions for di , xi such that the induced operator from l 2 → l 2 and related operators are well-defined, bounded, or compact. Furthermore, we give conditions, when this operator is injective and ill-posed.
Published Version
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