Search Results

You are looking at 1 - 10 of 1,740 items for :

  • "?-summability" x
Clear All

Abstract  

A general summability method of orthogonal series is given with the help of an integrable function Θ. Under some conditions on Θ we show that if the maximal Fejér operator is bounded from a Banach space X to Y, then the maximal Θ-operator is also bounded. As special cases the trigonometric Fourier, Walsh, Walsh--Kaczmarz, Vilenkin and Ciesielski--Fourier series and the Fourier transforms are considered. It is proved that the maximal operator of the Θ-means of these Fourier series is bounded from H p to L p (1/2<p≤; ∞) and is of weak type (1,1). In the endpoint case p=1/2 a weak type inequality is derived. As a consequence we obtain that the Θ-means of a function fL 1 converge a.e. to f. Some special cases of the Θ-summation are considered, such as the Weierstrass, Picar, Bessel, Riesz, de la Vallée-Poussin, Rogosinski and Riemann summations. Similar results are verified for several-dimensional Fourier series and Hardy spaces.

Restricted access

of some Fundamental Theorems of Summability Theory, Int. J. Math. & Math. Sci. 23(1) (2000), 1–9. MR 2001d :40006a Patterson R. F. Analogues of some Fundamental Theorems

Restricted access

Adolphson, A. and Sperber, S. , Exponential sums and Newton polyhedra: cohomology and estimates, Ann. of Math. (2), 130 (1989), no. 2, 367–406. Sperber

Restricted access

Erdös, P. and Szemerédi, E., On sums and products of integers, in: Studies in Pure Math. to the memory of P. Turán , Akadémiai Kiadó (Budapest, 1983), 213-218. MR 86m :11011

Restricted access

References [1] A nnaby , M. H. and A sharabi , R. M. , Exact evaluations of finite trigonometric sums by sampling theorems , Acta Math. Sci. Ser. B , 31 ( 2

Restricted access

numbers 1965 Hua, L. K. , On the representations of a number as the sum of two cubes, Math. Z. , 44

Restricted access

681 Banks, W. and Shparlinski, I. E. , Congruences and exponential sums with the Euler function, High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie

Restricted access

Abstract  

Let χ be a primitive multiplicative character modulo an integer m ≥ 1. Using some classical bounds of character sums, we estimate the average value of the character sums with subsequence sums

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$T_m (\mathcal{S},\chi ) = \sum\nolimits_{\mathcal{I} \subseteq \{ 1, \ldots ,N\} } {\chi (\sum\nolimits_{i \in \mathcal{I}} {s_i } )}$$ \end{document}
taken over all N-element sequences S = (s 1, …, s N) of integer elements in a given interval [K + 1, K + L]. In particular, we show that T m(S, χ) is small on average over all such sequences. We apply it to estimating the number of perfect squares in subsequence sums in almost all sequences.

Restricted access
Acta Mathematica Hungarica
Authors: Alfred Geroldinger, David J. Grynkiewicz and Wolfgang A. Schmid

References [1] Adhikari , S. D. , Grynkiewicz , D. J. and Sun , Z.-W. , On weighted zero-sum sequences , manuscript. [2

Restricted access

. [4] Motallebi M. R. , Locally convex product and direct sum cones , Mediterr. J. Math. , 11 ( 3 ) ( 2014 ), 913 – 927 . [5

Restricted access