منابع مشابه
Double Sequences and Double Series
This research considers two traditional important questions, which are interesting, at least to most mathematicians. The first question arises in the theory of double sequences of complex numbers, which concerns the relationship, if any, between the following three limits of a double sequence s : N×N −→ C: 1. limn,m→∞ s(n, m), 2. limn→∞(limm→∞ s(n, m)), 3. limm→∞(limn→∞ s(n, m)). In particular,...
متن کاملOperators and Divergent Series
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...
متن کاملOn 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 کاملDivergent Perturbation Series
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 sequences of Kleinian groups
One of the basic problems in studying topological structures of deformation spaces for Kleinian groups is to find a criterion to distinguish convergent sequences from divergent sequences. In this paper, we shall give a sufficient condition for sequences of Kleinian groups isomorphic to surface groups to diverge in the deformation spaces. AMS Classification 57M50; 30F40
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1926
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1926-1501332-5