Several arguments are given for the summability of the superstring perturbation series. Whereas the Schottky group coordinatization of moduli space may be used to provide refined estimates of large-order bosonic string amplitudes, the super-Schottky group variables define a measure for the supermoduli space integral which leads to upper bounds on superstring scattering amplitudes. The genus-dep...

1. Let 5= {$»} denote an infinite sequence of complex numbers and let A=*(ank) be a summation matrix. If the A -transform of s, {*n} = { X)*°-o nkSk} is a bounded sequence, it may be regarded as a bounded continuous function t(n) on the discrete space of natural numbers N, and thus it has a continuous extension 1 to /3iV, the StoneCech compactification of N$ cf. [2, pp. 82-95]. Let 7 o be a fix...

A simple structure of the multiple Laguerre polynomial expansions is used to study the Cesàro summability above the critical index for the convolution type Laguerre expansions. The multiple Laguerre polynomial expansion of an `1-radial function f0(|x|) is shown to be an `1-radial function that coincides with the Laguerre polynomial expansion of f0, which allows us to settle the problem of summa...

In this paper, we have proved two main theorems under more weaker conditions dealing with absolute weighted arithmetic mean summability factors of infinite series and trigonometric Fourier series. We also obtained certain new results on the different methods.

The concept of a spectral triple (unbounded Fredholm module) due to A.Connes ([Co1]) is a natural noncommutative generalisation of a notion of a compact manifold, with certain summability properties corresponding in the classical case to the dimension of the manifold. Recently E.Christensen and C. Ivan established the existence of spectral triples on arbitrary AF algebras ([CI]). In this note w...

A new theorem on almost generalized Nörlund summability of conjugate series of Fourier series has been established under a very general condition. 2000 Mathematics Subject Classification. Primary 42B05, 42B08.

In this paper, we obtain some conditions on a sequence under which subsequential convergence [Math. Morav. 5, 19-56 (2001; Zbl 1047.40005)] of the sequence follows from its (A, m) summability.

A BMO-estimation of two-dimensional Walsh-Fourier series is proved from which an almost everywhere exponential summability of quadratic partial sums of double Walsh-Fourier series is derived.

Zhizhiashvili proved sufficient condition for the Cesáro summability by negative order of N-multiple trigonometric Fourier series in the space L, 1 ≤ p ≤ ∞. In this paper we show that this condition cannot be improved .

In this paper we have improved the result of Bor [Bull. Math. Anal. Appl.1, (2009), 15-21] on local property of N, pn, θn k summability of factored Fourier series by proving under weaker conditions.