Quite recently, Savaş 1 obtained sufficient conditions for ∑ anλn to be summable |A, δ|k, k ≥ 1, 0 ≤ δ < 1/k. The purpose of this paper is to obtain the corresponding result for quasif-increasing sequence. Our result includes and moderates the conditions of his theorem with the special case μ 0. A sequence {λn} is said to be of bounded variation bv if ∑ n |Δλn| < ∞. Let bv0 bv ∩ c0, where c0 de...

is that of suitably defining a trigonometric integral with the property that, if the series (1.1) converges everywhere to a function ƒ(x), then f(x) is necessarily integrable and the coefficients, an and bn, given in the usual Fourier form. It is well known that a series may converge everywhere to a function which is not Lebesgue summable nor even Denjoy integrable (completely totalisable, [3])...

It is shown that the differential equation u(n) = p(t)u, where n ≥ 2 and p : [a, b] → R is a summable function, is not conjugate in the segment [a, b], if for some l ∈ {1, . . . , n− 1} , α ∈]a, b[ and β ∈]α, b[ the inequalities n ≥ 2 + 1 2 (1 + (−1)n−l), (−1)n−lp(t) ≥ 0 for t ∈ [a, b],

This paper is a study of summability methods that are based on the Riemann Zeta function. A limitation theorem is proved which gives a necessary condition for a sequence x to be zeta summable. A zeta summability matrix Z associated with a real sequence is introduced; a necessary and sufficient condition on the sequence such that Z maps 11 to 11 is established. Results comparing the strength of ...

We consider a variation of O(N)-symmetric vector models in which the vector components are Grassmann numbers. We show that these theories generate the same sort of random polymer models as the O(N) vector models and that they lie in the same universality class in the large-N limit. We explicitly construct the double-scaling limit of the theory and show that the genus expansion is an alternating...

is absolutely convergent and has the sum s . Then, as is well known, every rearrangement, S' a ;, of (1) also converges and has the same sum s . If, however, (1) n=1 converges, but not absolutely, then, according to Riemann's classical rearrangement theorem [3, p . 235, or 2, p . 318j, for every real number s', there exists a rearrangement of (1) whose sum is s' . Assume, now, that (1) is C 1-s...

In [2] Fan and Pollicott gave an estimate of convergence speed of the iterations fSn g fgn=1 ( Sg being the Ruelle operator de ̄ned by a normalized summable variation potential function g on a subshift of ̄nite type.) Later on Fan and Jiang [1] extended it to locally expansive Dini dynamical system. It is known that the systems they considered have the bounded distortion property (BDP). We extend...