منابع مشابه
Stieltjes Transforms on New Generalized Functions
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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Abstract. We have combined the Laplace transform and the Stieltjes transform of the form f̂(x) = R∞ 0 f(t) (xm+tm)ρ dt, m, ρ > 0 and applied it to an ordered vector space of generalized functions to which the topology of bounded convergence is assigned. Some of the order properties of the transform and its inverse are studied. Also we solve an initial value problem and compare different solution...
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We present the exact solution for a set of nonlinear algebraic equations 1 zl = πd + 2d n ∑ m6=l 1 zl−zm . These were encountered by us in a recent study of the low energy spectrum of the Heisenberg ferromagnetic chain [1]. These equations are low d (density) “degenerations” of more complicated transcendental equation of Bethe’s Ansatz for a ferromagnet, but are interesting in themselves. They ...
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We express the generalized Cauchy-Stieltjes transforms (GCST) of some particular Beta distributions depending on a positive parameter λ as λ-powered Cauchy-Stieltjes transforms (CST) of some probability measures. The CST of the latter measures are shown to be the geometric mean of the CST of the Wigner law together with another one. Moreover, they are absolutely continuous and we derive their d...
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ژورنال
عنوان ژورنال: Constructive Approximation
سال: 2018
ISSN: 0176-4276,1432-0940
DOI: 10.1007/s00365-018-9440-8