Seminars

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ABSTRACT: There are two notions of Square Root Problems: one is for probability measures and the other is for operators. In the first talk we consider the following Square Root Problem for probability measures: Given a positive probability Borel measure µ (supported on an interval [a, b ] ⊆ R +), does there exist a positive Borel measure ν such that µ = ν ∗ ν holds? (Here ∗ denotes the multiplicative convolution, properly defined on R +.) This problem is closely connected to the subnormality of the Aluthge transform of a unilateral weighted shift. We develop a criterion to test whether a measure µ admits a square root, and we provide a concrete solution for the case of a finitely atomic measure having at most six atoms.