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Wyszukujesz frazę "Móricz, Ferenc" wg kryterium: Autor

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    Wyświetlanie 1-7 z 7
    Tytuł:
    On the bundle convergence of double orthogonal series in noncommutative $L_2$-spaces
    Autorzy:
    Móricz, Ferenc
    Le Gac, Barthélemy
    Powiązania:
    https://bibliotekanauki.pl/articles/1206079.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    von Neumann algebra
    faithful and normal state
    completion
    Gelfand-Naimark-Segal representation theorem
    bundle convergence
    almost sure convergence
    regular convergence
    orthogonal sequence of vectors in $L_2$
    Rademacher-Men'shov theorem
    convergence in Pringsheim's sense
    Opis:
    The notion of bundle convergence in von Neumann algebras and their $L_2$-spaces for single (ordinary) sequences was introduced by Hensz, Jajte, and Paszkiewicz in 1996. Bundle convergence is stronger than almost sure convergence in von Neumann algebras. Our main result is the extension of the two-parameter Rademacher-Men'shov theorem from the classical commutative case to the noncommutative case. To our best knowledge, this is the first attempt to adopt the notion of bundle convergence to multiple series. Our method of proof is different from the classical one, because of the lack of the triangle inequality in a noncommutative von Neumann algebra. In this context, bundle convergence resembles the regular convergence introduced by Hardy in the classical case. The noncommutative counterpart of convergence in Pringsheim's sense remains to be found.
    Źródło:
    Studia Mathematica; 2000, 140, 2; 177-190
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the maximal Fejér operator for double Fourier series of functions in Hardy spaces
    Autorzy:
    Móricz, Ferenc
    Powiązania:
    https://bibliotekanauki.pl/articles/1288938.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Opis:
    We consider the Fejér (or first arithmetic) means of double Fourier series of functions belonging to one of the Hardy spaces $H^{(1,0)}(^2)$, $H^{(0,1)}(\mathbb{T}^2)$, or $H^{(1,1)}(\mathbb{T}^2)$. We prove that the maximal Fejér operator is bounded from $H^{(1,0)}(\mathbb{T}^2)$ or $H^{(0,1)}(\mathbb{T}^2)$ into weak-$L^1(\mathbb{T}^2)$, and also bounded from $H^{(1,1)}(\mathbb{T}^2)$ into $L^1(\mathbb{T}^2)$. These results extend those by Jessen, Marcinkiewicz, and Zygmund, which involve the function spaces $L^{1} log^{+} L(\mathbb{T}^2)$, $L^1(log^{+}L)^2(\mathbb{T}^2)$, and $L^μ(\mathbb{T}^2)$ with 0 < μ < 1, respectively. We establish analogous results for the maximal conjugate Fejér operators. On closing, we formulate two conjectures.
    Źródło:
    Studia Mathematica; 1995, 116, 1; 89-100
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the uniform convergence and L¹-convergence of double Walsh-Fourier series
    Autorzy:
    Móricz, Ferenc
    Powiązania:
    https://bibliotekanauki.pl/articles/1293178.pdf
    Data publikacji:
    1992
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Walsh-Paley system
    W-continuity
    moduli of continuity and smoothness
    bounded variation in the sense of Hardy and Krause
    generalized bounded variation
    complementary functions in the sense of W. H. Young
    rectangular partial sum
    Dirichlet kernel
    convergence in $L^p$-norm
    uniform convergence Salem's test
    Dini-Lipschitz test
    Dirichlet-Jordan test
    Opis:
    In 1970 C. W. Onneweer formulated a sufficient condition for a periodic W-continuous function to have a Walsh-Fourier series which converges uniformly to the function. In this paper we extend his results from single to double Walsh-Fourier series in a more general setting. We study the convergence of rectangular partial sums in $L^p$-norm for some 1 ≤ p ≤ ∞ over the unit square [0,1) × [0,1). In case p = ∞, by $L^p$ we mean $C_W$, the collection of uniformly W-continuous functions f(x, y), endowed with the supremum norm. As special cases, we obtain the extensions of the Dini-Lipschitz test and the Dirichlet-Jordan test for double Walsh-Fourier series.
    Źródło:
    Studia Mathematica; 1992, 102, 3; 225-237
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Tauberian theorems for Cesàro summable double integrals over $ℝ_{+}^{2}$
    Autorzy:
    Móricz, Ferenc
    Powiązania:
    https://bibliotekanauki.pl/articles/1206180.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Opis:
    Given ⨍ ∈ $L_\text{loc}^1 (ℝ_+^2)$, denote by s(w,z) its integral over the rectangle [0,w]× [0,z] and by σ(u,v) its (C,1,1) mean, that is, the average value of s(w,z) over [0,u] × [0,v], where u,v,w,z>0. Our permanent assumption is that (*) σ(u,v) → A as u,v → ∞, where A is a finite number. First, we consider real-valued functions ⨍ and give one-sided Tauberian conditions which are necessary and sufficient in order that the convergence (**) s(u,v) → A as u,v → ∞ follow from (*). Corollaries allow these Tauberian conditions to be replaced either by Schmidt type slow decrease (or increase) conditions, or by Landau type one-sided Tauberian conditions. Second, we consider complex-valued functions and give a two-sided Tauberian condition which is necessary and sufficient in order that (**) follow from (*). In particular, this condition is satisfied if s(u,v) is slowly oscillating, or if f(x,y) obeys Landau type two-sided Tauberian conditions. At the end, we extend these results to the mixed case, where the (C, 1, 0) mean, that is, the average value of s(w,v) with respect to the first variable over the interval [0,u], is considered instead of $σ_11 (u,v) := σ(u,v)$
    Źródło:
    Studia Mathematica; 2000, 138, 1; 41-52
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Tauberian theorems for Cesàro summable double sequences
    Autorzy:
    Móricz, Ferenc
    Powiązania:
    https://bibliotekanauki.pl/articles/1290321.pdf
    Data publikacji:
    1994
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    double sequence
    convergence in Pringsheim's sense
    summability (C,1,1)
    (C,1,0) and (C,0,1)
    one-sided Tauberian condition of Landau and Hardy type
    slow decrease
    ordered linear space
    Opis:
    $(s_{jk}: j,k = 0,1,...)$ be a double sequence of real numbers which is summable (C,1,1) to a finite limit. We give necessary and sufficient conditions under which $(s_{jk})$ converges in Pringsheim's sense. These conditions are satisfied if $(s_{jk})$ is slowly decreasing in certain senses defined in this paper. Among other things we deduce the following Tauberian theorem of Landau and Hardy type: If $(s_{jk})$ is summable (C,1,1) to a finite limit and there exist constants $n_1 > 0$ and H such that $jk(s_{jk} - s_{j-1,k} - s_{j-1,k} + s_{j-1,k-1}) ≥ -H$, $j(s_{jk} - s_{j-1, k}) ≥ -H$ and $k(s_{jk} - s_{j,k-1}) ≥ -H$ whenever $j,k > n_1$, then $(s_{jk})$ converges. We always mean convergence in Pringsheim's sense. Our method is suitable to obtain analogous Tauberian results for double sequences of complex numbers or for those in an ordered linear space over the real numbers.
    Źródło:
    Studia Mathematica; 1994, 110, 1; 83-96
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-7 z 7

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