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.

In this paper we prove the local L s regularity (where s depends on the summability of the data) for local " unbounded " weak solutions of a class of nonlinear parabolic equations including the p-Laplacian equation.

In this paper we prove a theorem concerning the relative strength of \R,P„\k and \R,qn\k summability methods, k > 1 , that generalizes a result of Bosanquet [1].

In this paper the concept of strongly (λM )p − Cesáro summability of a sequence of fuzzy numbers and strongly λM− statistically convergent sequences of fuzzy numbers is introduced. Keywords—Fuzzy numbers, statistical convergence, Orlicz space, gai sequence.