Almost everywhere summability of Laguerre series. II

K. Stempak

Displaying similar documents to “Almost everywhere summability of Laguerre series. II”

Almost everywhere convergence of some summabillity methods for Laguerre series

Jolanta Długosz (1985)

Studia Mathematica

Similarity:

Almost everywhere convergence of Laguerre series

Chang-Pao Chen, Chin-Cheng Lin (1994)

Studia Mathematica

Similarity:

Hermite expansions on R for radial functions.

Sundaram Thangavelu (1990)

Revista Matemática Iberoamericana

Similarity:

Solving dual integral equations on Lebesgue spaces

Óscar Ciaurri, José Guadalupe, Mario Pérez, Juan Varona (2000)

Studia Mathematica

Similarity:

We study dual integral equations associated with Hankel transforms, that is, dual integral equations of Titchmarsh’s type. We reformulate these equations giving a better description in terms of continuous operators on $L^{p}$ spaces, and we solve them in these spaces. The solution is given both as an operator described in terms of integrals and as a series $\sum_{n = 0}^{\infty} c_{n} J_{μ + 2 n + 1}$ which converges in the $L^{p}$ -norm and almost everywhere, where $J_{ν}$ denotes the Bessel function of order ν. Finally, we study the uniqueness...

On a Summability Method Defined by Means of Hermite Polynomials Върху един метод на сумиране, дефиниран чрез полиномите на Ермит

Boychev, Georgi (2012)

Union of Bulgarian Mathematicians

Similarity:

Георги С. Бойчев - В статията се разглежда метод за сумиране на редове, дефиниран чрез полиномите на Ермит. За този метод на сумиране са дадени някои Тауберови теореми. A summability method, defined by mean of the Hermite polynomials, is proposed. For this summation method Tauberian theorems are given. *2000 Mathematics Subject Classification: 33C45, 40G05.

Expansions of solutions to a hypoelliptic differential equation in terms of polynomiallike solutions

Biesterfeldt, H.J. jr. (1966)

Portugaliae mathematica

Similarity:

Properties of the orthonormal Franklin system

Z. Ciesielski (1963)

Studia Mathematica

Similarity:

Equisummability Theorems for Laguerre Series

Abd El-Aal El-Adad, El-Sayed (1996)

Serdica Mathematical Journal

Similarity:

Here we prove results about Riesz summability of classical Laguerre series, locally uniformly or on the Lebesgue set of the function f such that (∫(1 + x)^(mp) |f(x)|^p dx )^(1/p) < ∞, for some p and m satisfying 1 ≤ p ≤ ∞, −∞ < m < ∞.

A new type of polynomials approximating a continuous or integrable function

L. Hsu (1959)

Studia Mathematica

Similarity:

Almost everywhere summability of Laguerre series

Krzysztof Stempak (1991)

Studia Mathematica

Similarity:

We apply a construction of generalized twisted convolution to investigate almost everywhere summability of expansions with respect to the orthonormal system of functions $ℓ_{n}^{a} (x) = {(n! / Γ (n + a + 1))}^{1 / 2} e^{- x / 2} L_{n}^{a} (x)$ , n = 0,1,2,..., in $L^{2} (ℝ_{+}, x^{a} d x)$ , a ≥ 0. We prove that the Cesàro means of order δ > a + 2/3 of any function $f \in L^{p} (x^{a} d x)$ , 1 ≤ p ≤ ∞, converge to f a.e. The main tool we use is a Hardy-Littlewood type maximal operator associated with a generalized Euclidean convolution.

Quadratic tilt-excess decay and strong maximum principle for varifolds

Reiner Schätzle (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

In this paper, we prove that integral $n$ -varifolds $μ$ in codimension 1 with $H_{μ} \in L_{loc}^{p} (μ)$ , $p > n$ , $p \geq 2$ have quadratic tilt-excess decay ${tiltex}_{μ} (x, ϱ, T_{x} μ) = O_{x} (ϱ^{2})$ for $μ$ -almost all $x$ , and a strong maximum principle which states that these varifolds cannot be touched by smooth manifolds whose mean curvature is given by the weak mean curvature $H_{μ}$ , unless the smooth manifold is locally contained in the support of $μ$ .