The Killip–simon Theorem: Szegő for Oprl
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چکیده
By structure of the set of solutions, we mean is it closed in the weak topology? (This is not obvious since x is not bounded.) Is it of finite or infinite dimension? Among the solutions, are there any that are pure point or singular continuous or purely absolutely continuous? If there exists a unique solution, we call the moment problem determinate, and if there are multiple solutions, indeterminate. Since we can replace cn by cn/c0, we can and will always suppose that c0 = 1. Often the cn are given by (3.8.1), so existence is trivial. The moment problem then becomes:
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