Generalized Stieltjes functions and their exact order
نویسندگان
چکیده
منابع مشابه
Real-variables characterization of generalized Stieltjes functions
We obtain a characterization of generalized Stieltjes functions of any order λ > 0 in terms of inequalities for their derivatives on (0,∞). When λ = 1, this provides a new and simple proof of a characterization of Stieltjes functions first obtained by Widder in 1938.
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We introduce a Stieltjes transform on the equivalence classes of a new generalized function which has been successfully developed by Colombeau. Subsets of rapid descent test functions, (Rn), as well as tempered distributions, ′(Rn), are used to preserve Fourier analysis techniques. 2000 Mathematics Subject Classification. Primary 46F12.
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The generalized Stieltjes transform (GST) is an integral transform that depends on a parameter ρ > 0. In previous work a convenient form of the inverse transformation was derived for the case ρ = 3/2. This paper generalizes that result to all ρ > 0. It is a well-known fact that the GST can be formulated as an iterated Laplace transform, and that therefore its inverse can be expressed as an iter...
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ژورنال
عنوان ژورنال: Journal of Classical Analysis
سال: 2012
ISSN: 1848-5987
DOI: 10.7153/jca-01-07