A non-hyponormal operator generating Stieltjes moment sequences
نویسندگان
چکیده
منابع مشابه
On powers of Stieltjes moment sequences, I
For a Bernstein function f the sequence sn = f(1)·. . .·f(n) is a Stieltjes moment sequence with the property that all powers sn, c > 0 are again Stieltjes moment sequences. We prove that sn is Stieltjes determinate for c ≤ 2, but it can be indeterminate for c > 2 as is shown by the moment sequence (n!)c, corresponding to the Bernstein function f(s) = s. Nevertheless there always exists a uniqu...
متن کاملOn powers of Stieltjes moment sequences, II
We consider the set of Stieltjes moment sequences, for which every positive power is again a Stieltjes moment sequence, we and prove an integral representation of the logarithm of the moment sequence in analogy to the Lévy-Khintchine representation. We use the result to construct product convolution semigroups with moments of all orders and to calculate their Mellin transforms. As an applicatio...
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For a certain constant δ > 0 (a little less than 1/4), every function f : N0 → ]0,∞[ satisfying f(n)2 ≤ δf(n − 1)f(n + 1), n ∈ N, is a Stieltjes indeterminate Stieltjes moment sequence. For every indeterminate moment sequence f : N0 → R there is a positive definite matrix sequence (an) which is not of positive type and which satisfies tr(an+2) = f(n), n ∈ N0. For a certain constant ε > 0 (a lit...
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We introduce a non-linear injective transformation T from the set of non-vanishing normalized Hausdorff moment sequences to the set of normalized Stieltjes moment sequences by the formula T [(an)]n = 1/(a1 · . . . · an). Special cases of this transformation have appeared in various papers on exponential functionals of Lévy processes, partly motivated by mathematical finance. We give several exa...
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The class of generating functions for completely monotone sequences (moments of finite positive measures on [0, 1]) has an elegant characterization as the class of Pick functions analytic and positive on (−∞, 1). We establish this and another such characterization and develop a variety of consequences. In particular, we characterize generating functions for moments of convex and concave probabi...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2012
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2012.02.006