Nearness of continued fractions.
Nearness relations in linear spaces
In this paper, we consider nearness-based convergence in a linear space, where the coordinatewise given nearness relations are aggregated using weighted pseudo-arithmetic and geometric means and using continuous t-norms.
Necessary and sufficient conditions for joint lower and upper estimates.
Necessary and sufficient conditions for matrix summability methods to be stronger than multisummability
For general matrix summability methods, we find necessary and sufficient conditions for such methods to be stronger than multisummability. In a second part we show the existence of power series which are not multisummable but can be summed by a matrix method satisfying the conditions mentioned above
Necessary and sufficient conditions under which convergence follows from summability by weighted means.
Necessary and sufficient Tauberian conditions for the logarithmic summability of functions and sequences
Let s: [1,∞) → ℂ be a locally Lebesgue integrable function. We say that s is summable (L,1) if there exists some A ∈ ℂ such that , where . (*) It is clear that if the ordinary limit s(t) → A exists, then also τ(t) → A as t → ∞. We present sufficient conditions, which are also necessary, in order that the converse implication hold true. As corollaries, we obtain so-called Tauberian theorems which are analogous to those known in the case of summability (C,1). For example, if the function s is slowly...
Negative Resultate über Tauber-Bedingungen.
Několik poznámek o řetězcích
Nested derivatives: a simple method for computing series expansions of inverse functions.
New results in discrete asymptotic analysis.
Newer applications of generalized monotone sequences.
Nilakantha's accelerated series for π
We show how the idea behind a formula for π discovered by the Indian mathematician and astronomer Nilakantha (1445-1545) can be developed into a general series acceleration technique which, when applied to the Gregory-Leibniz series, gives the formula with convergence as , in much the same way as the Euler transformation gives with convergence as . Similar transformations lead to other accelerated series for π, including three “BBP-like” formulas, all of which are collected in the Appendix....
Nonabsolutely convergent series
Assume that for any from an interval a real number is given. Summarizing all these numbers is no problem in case of an absolutely convergent series . The paper gives a rule how to summarize a series of this type which is not absolutely convergent, using a theory of generalized Perron (or Kurzweil) integral.
Non-embeddability of general unipotent diffeomorphisms up to formal conjugacy
The formal class of a germ of diffeomorphism is embeddable in a flow if is formally conjugated to the exponential of a germ of vector field. We prove that there are complex analytic unipotent germs of diffeomorphisms at () whose formal class is non-embeddable. The examples are inside a family in which the non-embeddability is of geometrical type. The proof relies on the properties of some linear functional operators that we obtain through the study of polynomial families of diffeomorphisms...
Noninclusion theorems for summability matrices.
Noninclusion theorems: Some remarks on a paper by J. A. Fridy.
Non-Replaceable Matrices.
Nörlund Summability of Jacobi and Laguerre series.
Norm and lower bounds of operators on weighted sequence spaces
Norm-preserving L-L integral transformations.