منابع مشابه
On Absolutely Divergent Series
We show that in the א2-stage countable support iteration of Mathias forcing over a model of CH the complete Boolean algebra generated by absolutely divergent series under eventual dominance is not isomorphic to the completion of P (ω)/fin. This complements Vojtáš’ result, that under cf(c) = p the two algebras are isomorphic [15].
متن کاملNeutrix Limit on Divergent Series
In this paper, we give a simple and straight forward definition for the neutrix limit of divergent series and use it to study the neutrix limits of the divergent series ralated to the Rieman-Zeta function ζ(α) and some series related to the polylogarith function Lin(z). Then, we apply the reults to some specific examles. Our reults on Riemann-Zeta function and its derivatives are consistent wit...
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We give a natural extension of the classical definition of Césaro convergence of a divergent sequence/function. This involves understanding the spectrum of eigenvalues and eigenvectors of a certain Césaro operator on a suitable space of functions or sequences. The essential idea is applicable in identical fashion to other summation methods such as Borel’s. As an example we show how to obtain th...
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Various perturbation series are factorially divergent. The behavior of their high-order terms can be found by Lipatov’s method, according to which they are determined by instanton configurations of appropriate functional integrals. When the Lipatov asymptotics is known and several lowest order terms of the perturbation series are found by direct calculation of diagrams, one can gain insight int...
متن کاملDivergent Legendre-sobolev Polynomial Series
Let be introduced the Sobolev-type inner product (f, g) = 1 2 Z 1 −1 f(x)g(x)dx + M [f ′(1)g′(1) + f ′(−1)g′(−1)], where M ≥ 0. In this paper we will prove that for 1 ≤ p ≤ 4 3 there are functions f ∈ L([−1, 1]) whose Fourier expansion in terms of the orthonormal polynomials with respect to the above Sobolev inner product are divergent almost everywhere on [−1, 1]. We also show that, for some v...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1895
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1895-00314-6