Total Positivity in Stable Semigroups

Simon, Thomas

doi:10.1007/s00365-016-9337-3

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2018

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“…for every n ≥ 1, the case n = 0 being evaluated in the above (12). Plugging all these expressions into (13) and switching the two finite sums, we get…”

Section: (B)mentioning

confidence: 99%

Stieltjes functions of finite order and hyperbolic monotonicity

Bondesson

Simon

2018

Trans. Amer. Math. Soc.

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A class of Stieltjes functions of finite type is introduced. These satisfy Widder's conditions on the successive derivatives up to some finite order, and are not necessarily smooth. We show that such functions have a unique integral representation, along some generic kernel which is a truncated Laurent series approximating the standard Stieltjes kernel. We then obtain a two-to-one correspondence, via the logarithmic derivative, between these functions and a subclass of hyperbolically monotone functions of finite type. This correspondence generalizes a representation of HCM functions in terms of two Stieltjes transforms earlier obtained by the first author.2010 Mathematics Subject Classification. 44A15, 60E10.

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“…for every n ≥ 1, the case n = 0 being evaluated in the above (12). Plugging all these expressions into (13) and switching the two finite sums, we get…”

Section: (B)mentioning

confidence: 99%