Almost everywhere convergence of some summabillity methods for Laguerre series
Jolanta Długosz (1985)
Studia Mathematica
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Jolanta Długosz (1985)
Studia Mathematica
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Chang-Pao Chen, Chin-Cheng Lin (1994)
Studia Mathematica
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Sundaram Thangavelu (1990)
Revista Matemática Iberoamericana
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Óscar Ciaurri, José Guadalupe, Mario Pérez, Juan Varona (2000)
Studia Mathematica
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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 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 which converges in the -norm and almost everywhere, where denotes the Bessel function of order ν. Finally, we study the uniqueness...
Boychev, Georgi (2012)
Union of Bulgarian Mathematicians
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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.
Biesterfeldt, H.J. jr. (1966)
Portugaliae mathematica
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Z. Ciesielski (1963)
Studia Mathematica
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Abd El-Aal El-Adad, El-Sayed (1996)
Serdica Mathematical Journal
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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 < ∞.
L. Hsu (1959)
Studia Mathematica
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Krzysztof Stempak (1991)
Studia Mathematica
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We apply a construction of generalized twisted convolution to investigate almost everywhere summability of expansions with respect to the orthonormal system of functions , n = 0,1,2,..., in , a ≥ 0. We prove that the Cesàro means of order δ > a + 2/3 of any function , 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.
Reiner Schätzle (2004)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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In this paper, we prove that integral -varifolds in codimension 1 with , , have quadratic tilt-excess decay for -almost all , 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 , unless the smooth manifold is locally contained in the support of .