On $|V,\lambda |$ summability of a factored Fourier series

P. L. Sharma; R. K. Jain

Displaying similar documents to “On $| V, λ |$ summability of a factored Fourier series”

On the inclusion relation between strong $(J, p_{n})$ and strong $(\bar{N}, p_{n})$ summability methods

R. K. Jain, A. Ganguly (1978)

Matematički Vesnik

Similarity:

Relations among K $S (λ)$ and certain other methods for evaluations of sequences and series

B. Martić (1964)

Matematički Vesnik

Similarity:

On the $C^{α} | C^{β}$ convergence

L. Jeśmanowicz (1962)

Annales Polonici Mathematici

Similarity:

On the Nörlund means of Vilenkin-Fourier series

István Blahota, Lars-Erik Persson, Giorgi Tephnadze (2015)

Czechoslovak Mathematical Journal

Similarity:

We prove and discuss some new $(H_{p}, L_{p})$ -type inequalities of weighted maximal operators of Vilenkin-Nörlund means with non-increasing coefficients ${q_{k} : k \geq 0}$ . These results are the best possible in a special sense. As applications, some well-known as well as new results are pointed out in the theory of strong convergence of such Vilenkin-Nörlund means. To fulfil our main aims we also prove some new estimates of independent interest for the kernels of these summability results. In the special cases of...

On $[F, d_{n}]$ summability of Fourier series

P. L. Sharma, V. Prakash, S. K. Varma (1985)

Matematički Vesnik

Similarity:

Multi-dimensional Fejér summability and local Hardy spaces

Ferenc Weisz (2009)

Studia Mathematica

Similarity:

It is proved that the multi-dimensional maximal Fejér operator defined in a cone is bounded from the amalgam Hardy space $W (h_{p}, ℓ_{\infty})$ to $W (L_{p}, ℓ_{\infty})$ . This implies the almost everywhere convergence of the Fejér means in a cone for all $f \in W (L ₁, ℓ_{\infty})$ , which is larger than $L ₁ (ℝ^{d})$ .

On the pointwise strong approximation by (C,1)(E,1) means

Włodzimierz Łenski, Bogdan Roszak (2008)

Banach Center Publications

Similarity:

We present an estimate of the (C,1)(E,1)-strong means with mixed powers of the Fourier series of a function $f \in L_{2 π}$ as a generalization of the result obtained by M. Yildrim and F. Karakus. Some corollaries on the norm approximation are also given.

Functions in $L_{p}$ -space and their approximations

P. Chandra (1988)

Matematički Vesnik

Similarity:

A note on the $[τ, f (x)]$ means

V. Swaminathan (1979)

Matematički Vesnik

Similarity:

Pointwise Fourier inversion of distributions on spheres

Francisco Javier González Vieli (2017)

Czechoslovak Mathematical Journal

Similarity:

Given a distribution $T$ on the sphere we define, in analogy to the work of Łojasiewicz, the value of $T$ at a point $ξ$ of the sphere and we show that if $T$ has the value $τ$ at $ξ$ , then the Fourier-Laplace series of $T$ at $ξ$ is Abel-summable to $τ$ .

Convergence of greedy approximation II. The trigonometric system

S. V. Konyagin, V. N. Temlyakov (2003)

Studia Mathematica

Similarity:

We study the following nonlinear method of approximation by trigonometric polynomials. For a periodic function f we take as an approximant a trigonometric polynomial of the form $G ₘ (f) : = \sum_{k \in Λ} f ̂ (k) e^{i (k, x)}$ , where $Λ \subset ℤ^{d}$ is a set of cardinality m containing the indices of the m largest (in absolute value) Fourier coefficients f̂(k) of the function f. Note that Gₘ(f) gives the best m-term approximant in the L₂-norm, and therefore, for each f ∈ L₂, ||f-Gₘ(f)||₂ → 0 as m → ∞. It is known from previous results that in...

Lebesgue type points in strong (C,α) approximation of Fourier series

Włodzimierz Łenski, Bogdan Roszak (2011)

Banach Center Publications

Similarity:

We present an estimation of the $H_{k ₀, k_{r}}^{q, α} f$ and $H_{λ, u}^{ϕ, α} f$ means as approximation versions of the Totik type generalization (see [5], [6]) of the result of G. H. Hardy, J. E. Littlewood. Some corollaries on the norm approximation are also given.

Extensions of weak type multipliers

P. Mohanty, S. Madan (2003)

Studia Mathematica

Similarity:

We prove that if $Λ \in M_{p} (ℝ^{N})$ and has compact support then Λ is a weak summability kernel for 1 < p < ∞, where $M_{p} (ℝ^{N})$ is the space of multipliers of $L^{p} (ℝ^{N})$ .

A note on a critical problem with natural growth in the gradient

Boumediene Abdellaoui, Ireneo Peral (2006)

Journal of the European Mathematical Society

Similarity:

The paper analyzes the influence on the meaning of natural growth in the gradient of a perturbation by a Hardy potential in some elliptic equations. Indeed, in the case of the Laplacian the natural problem becomes $- Δ u - Λ_{N} \frac{u}{{| x |}^{2}} = {|\nabla u + \frac{N - 2}{2} \frac{u}{{| x |}^{2}} x|}^{2} {| x |}^{(N - 2) / 2} + λ f (x)$ in $Ω$ , $u = 0$ on $\partial Ω$ , $Λ_{N} = {((N - 2) / 2)}^{2}$ . This problem is a particular case of problem (2). Notice that $(N - 2) / 2$ is optimal as coefficient and exponent on the right hand side.

Generalized absolute convergence of single and double Vilenkin-Fourier series and related results

Nayna Govindbhai Kalsariya, Bhikha Lila Ghodadra (2024)

Mathematica Bohemica

Similarity:

We consider the Vilenkin orthonormal system on a Vilenkin group $G$ and the Vilenkin-Fourier coefficients $\hat{f} (n)$ , $n \in ℕ$ , of functions $f \in L^{p} (G)$ for some $1 < p \leq 2$ . We obtain certain sufficient conditions for the finiteness of the series $\sum_{n = 1}^{\infty} a_{n} {| \hat{f} (n) |}^{r}$ , where ${a_{n}}$ is a given sequence of positive real numbers satisfying a mild assumption and $0 < r < 2$ . We also find analogous conditions for the double Vilenkin-Fourier series. These sufficient conditions are in terms of (either global or local) moduli of continuity of $f$ and give multiplicative...

Some Tauberian theorems on $A_{λ}$ summability methods of integrals

B. P. Mishra, D. Singh (1976)

Matematički Vesnik

Similarity:

Estimates with global range for oscillatory integrals with concave phase

Bjorn Gabriel Walther (2002)

Colloquium Mathematicae

Similarity:

We consider the maximal function $| | (S^{a} f) [x] {| |}_{L^{\infty} [- 1, 1]}$ where $(S^{a} f) {(t)}^{\land} (ξ) = e^{{i t | ξ |}^{a}} f ̂ (ξ)$ and 0 < a < 1. We prove the global estimate $| | S^{a} f {| |}_{L ² (ℝ, L^{\infty} [- 1, 1])} {\leq C | | f | |}_{H^{s} (ℝ)}$ , s > a/4, with C independent of f. This is known to be almost sharp with respect to the Sobolev regularity s.

$L_{\infty}$ -Convergence of Finite Element Approximation

J. A. Nitsche (1975)

Publications mathématiques et informatique de Rennes

Similarity:

On the approximation of real continuous functions by series of solutions of a single system of partial differential equations

Carsten Elsner (2006)

Colloquium Mathematicae

Similarity:

We prove the existence of an effectively computable integer polynomial P(x,t₀,...,t₅) having the following property. Every continuous function $f : ℝ^{s} \to ℝ$ can be approximated with arbitrary accuracy by an infinite sum $\sum_{r = 1}^{\infty} H_{r} (x ₁, . . ., x_{s}) \in C^{\infty} (ℝ^{s})$ of analytic functions $H_{r}$ , each solving the same system of universal partial differential equations, namely $P (x_{σ}; H_{r}, \partial H_{r} / \partial x_{σ}, . . ., \partial ⁵ H_{r} / \partial x ⁵_{σ} ⁵) = 0$ (σ = 1,..., s).

Approximation of functions from $L^{p} {(ω ̃)}_{β}$ by linear operators of conjugate Fourier series

WŁodzimierz Łenski, Bogdan Szal (2011)

Banach Center Publications

Similarity:

We show the results corresponding to some theorems of S. Lal and H. K. Nigam [Int. J. Math. Math. Sci. 27 (2001), 555-563] on the norm and pointwise approximation of conjugate functions and to the results of the authors [Acta Comment. Univ. Tartu. Math. 13 (2009), 11-24] also on such approximations.

On $L^{p}$ integrability and convergence of trigonometric series

Dansheng Yu, Ping Zhou, Songping Zhou (2007)

Studia Mathematica

Similarity:

We first give a necessary and sufficient condition for $x^{- γ} ϕ (x) \in L^{p}$ , 1 < p < ∞, 1/p - 1 < γ < 1/p, where ϕ(x) is the sum of either $\sum_{k = 1}^{\infty} a_{k} c o s k x$ or $\sum_{k = 1}^{\infty} b_{k} s i n k x$ , under the condition that λₙ (where λₙ is aₙ or bₙ respectively) belongs to the class of so called Mean Value Bounded Variation Sequences (MVBVS). Then we discuss the relations among the Fourier coefficients λₙ and the sum function ϕ(x) under the condition that λₙ ∈ MVBVS, and deduce a sharp estimate for the weighted modulus of continuity of ϕ(x)...

Displaying similar documents to “On | V , λ | summability of a factored Fourier series”

Displaying similar documents to “On $| V, λ |$ summability of a factored Fourier series”