Results 131 to 140 of about 17,183,410 (158)

Almost Everywhere Convergence of Greedy Algorithm with Respect to Vilenkin System

Journal of Contemporary Mathematical Analysis, 2018
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M G Grigoryan
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Weighted average of dirichlet kernels for vilenkin-like system

Acta Mathematica Scientia, 2009
Abstract For Vilenkin-like system, the authors define a new operator H * f ≔ sup n | H n f |, where H n f is the weighted average for partial sums, and prove that H * is of type ( H* p ( G m ), L p ( G m )) for all ½ S* f ≔ | S n f | is of type (p,p) for 1 p > ∞, where S n f is the n -partial sum.
Peide Liu
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On the Parseval equality and the Dini-Lipschitz condition with respect to the Vilenkin system

Analysis Mathematica, 1984
The Parseval equality (*) \(\sum^{\infty}_{k=0}a_ k\bar l_ k=\) is true for the Fourier coefficients \(a_ k\), resp. \(l_ k\) of any elements f and g of a Hilbert space H with respect to any complete orthonormal system \(\Phi\) in H. If H stands for \(L^ 2(U)\) with the usual scalar product, where U is the so called Vilenkin group [N. Ya. Vilenkin, Izv.
exaly   +2 more sources

Uniqueness Theorems for Series by Vilenkin System

Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 2018
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Gevorkyan, G. G., Navasardyan, K. A.
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An integrability theorem for unbounded Vilenkin systems

Analysis Mathematica, 1997
We state the symmetry condition at the end of the first section, after specifying a construction of Vilenkin systems. In Section 2, we provide more information about these systems, and outline the proof of our main result. In Section 3, we complete the proof, except for two lemmas, which we prove in Section 4.
Aubertin, Bruce, Fournier, J. J. F.
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Paley Type Inequalities for Several Parameter Vilenkin Systems

Analysis Mathematica, 2001
In this paper the authors prove Paley type inequalities for two-parameter Vilenkin systems. Their main result is the following estimate: \[ \biggl(\sum_{n,k=0}^{\infty}(p_nq_k)^{1-2/p}(P_nQ_k)^{2-2/p}) \sum_{j=1}^{p_n-1}\sum_{l=1}^{q_k-1}|\hat f(jP_n,lQ_k)|^2\biggr)^{1/2} \leq C_p\|f\|_{H^p} \] for any martingale \(f\) in the Hardy space \(H^p(G_ ...
Simon, P., Weisz, F.
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Vilenkin systems and generalized triangular truncation operator

Integral Equations and Operator Theory, 2001
Let \(\widetilde{G}_N\) be the dual group of the Vilenkin group \(G_N\); we consider \(\widehat{G}_N\) ordered via the reverse lexicographical ordering. Let \(Q_n\) be the projection in \(L_p\) \((G_N, L_p({\mathcal M},\tau))\) on the eigenspace corresponding to \(\mathfrak n\), where \(L_p({\mathcal M},\tau)\) is the \(L_p\)-space associated with a ...
Dodds, P. G., Ferleger, S. V., de Pagter, B., Sukochev, F. A.   +3 more
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Orthonormal systems on Vilenkin groups

Acta Mathematica Hungarica, 1991
Let \(G_ m\) denote the topological product of a sequence of discrete cyclic groups \(Z_{m_ k}\) \((k\geq 0,m_ k\geq 2)\), with the direct product measure \(\mu\) given by the pointwise measures \(\mu_ k\) for which \(\mu_ k(j)=1/m_ k\) \((j\in Z_{m_ k})\). Starting with a certain particular complete and orthonormal system of characters \(\psi_ 0,\psi_
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On the lower bound of Sunouchi’s operator with respect to Vilenkin systems

Analysis Mathematica, 1997
Let \( m=(m_k,k\in {\mathbb N}\quad ({\mathbb N}:=\{ 0,1,\dots \})\), where \(m_k\in {\mathbb N}\), \(m_k\geq 2\). Then by definition \(G_m=\prod_{k=0}^{\infty} {\mathbb Z}_{m_k}\) and the group of characters for \(G_m\) is an orthonormal Vilenkin system. Let \(S_n f\) and \(\sigma_n f\) be the Vilenkin-Fourier sums and their Fejér means for \(f\in L^1(
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Hardy and Paley Inequalities for Fully-Odd Vilenkin Systems

Acta Mathematica Hungarica, 1997
Choose a nonatomic probability space \(\Omega\). Let \((\psi_n)^\infty_{n=-\infty}\) for be a Vilenkin system on \(\Omega\). Denote the probability measure on \(\Omega\) by \(d\omega\). Given a function \(f\) in \(L^1(d\omega)\) and an integer \(n\), let \[ \widehat f (n)=\int_\Omega f(\omega)\overline{\psi_n(\omega)}d\omega.
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