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Wyświetlanie 1-15 z 484
Tytuł:
Almost everywhere summability of Laguerre series
Autorzy:
Stempak, Krzysztof
Powiązania:
https://bibliotekanauki.pl/articles/1293496.pdf
Data publikacji:
1991
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Laguerre expansions
generalized twisted convolution
Riesz
Cesàro and Abel-Poisson means
Opis:
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 $L^2(ℝ_+, x^adx)$, a ≥ 0. We prove that the Cesàro means of order δ > a + 2/3 of any function $f ∈ L^p(x^adx)$, 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.
Źródło:
Studia Mathematica; 1991, 100, 2; 129-147
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Integral representations for some weighted classes of functions holomorphic in matrix domains
Autorzy:
Djrbashian, M.
Karapetyan, A.
Powiązania:
https://bibliotekanauki.pl/articles/1312519.pdf
Data publikacji:
1991
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Siegel domain
matrix domains
generalized unit disk
generalized upper half-plane
weighted classes of holomorphic functions
integral representations
Opis:
In 1945 the first author introduced the classes $H^p(α)$, 1 ≤ p<∞, α > -1, of holomorphic functions in the unit disk with finite integral (1) $ ∬_\mathbb{D} |f(ζ)|^p (1-|ζ|²)^α dξ dη < ∞ (ζ=ξ+iη) $ and established the following integral formula for $f ∈ H^p(α)$: (2) $ f(z) = (α+1)/π ∬_\mathbb{D} f(ζ) ((1-|ζ|²)^α)//((1-zζ̅)^{2+α}) dξdη, z∈ \mathbb{D} $. We have established that the analogues of the integral representation (2) hold for holomorphic functions in Ω from the classes $L^p(Ω;[K(w)]^α dm(w))$, where: 1) $Ω = {w = (w₁,...,w_n) ∈ ℂ^n: Im w₁ > ∑_{k=2}^n |w_k|²}$, $K(w) = Im w₁ - ∑_{k=2}^n |w_k|²$; 2) Ω is the matrix domain consisting of those complex m × n matrices W for which $I^{(m)} - W·W*$ is positive-definite, and $K(W) = det[I^{(m)} - W·W*]$; 3) Ω is the matrix domain consisting of those complex n × n matrices W for which $Im W = (2i)^{-1} (W - W*)$ is positive-definite, and K(W) = det[Im W]. Here dm is Lebesgue measure in the corresponding domain, $I^{(m)}$ denotes the unit m × m matrix and W* is the Hermitian conjugate of the matrix W.
Źródło:
Annales Polonici Mathematici; 1991, 55, 1; 87-94
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The generalization of some properties of universal matrices
Autorzy:
Hauke, Jan
Krzyszkowska, Jolanta
Powiązania:
https://bibliotekanauki.pl/articles/748120.pdf
Data publikacji:
1991
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Measures of association
Matrix inversion, generalized inverses
Linear regression
Opis:
.
We consider an k x k universal matrix G introduced by Hellwig (1976). We analyze two problems: the nonsingularity of the matrix G and the sign-consistency of the elements of the vector r = (ri) and of the solutrion b = (bi) to the system Gb = r. Obtained results generalize the results presented by Kolupa (1977, 1980).
Źródło:
Mathematica Applicanda; 1991, 20, 34
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized solutions to boundary value problems for quasilinear hyperbolic systems of partial differential-functional equations
Autorzy:
Człapiński, Tomasz
Powiązania:
https://bibliotekanauki.pl/articles/1312033.pdf
Data publikacji:
1992
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
differential-functional system
second canonical form
generalized solutions
Opis:
Generalized solutions to quasilinear hyperbolic systems in the second canonical form are investigated. A theorem on existence, uniqueness and continuous dependence upon the boundary data is given. The proof is based on the methods due to L. Cesari and P. Bassanini for systems which are not functional.
Źródło:
Annales Polonici Mathematici; 1992, 57, 2; 177-191
0066-2216
Pojawia się w:
Annales Polonici Mathematici
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:
On Lie algebras of vector fields related to Riemannian foliations
Autorzy:
Rybicki, Tomasz
Powiązania:
https://bibliotekanauki.pl/articles/1311816.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Riemannian foliation
Lie algebra
ideal
isomorphism
vector field
generalized manifold
stratification
Opis:
Riemannian foliations constitute an important type of foliated structures. In this note we prove two theorems connecting the algebraic structure of Lie algebras of foliated vector fields with the smooth structure of a Riemannian foliation.
Źródło:
Annales Polonici Mathematici; 1993, 58, 2; 111-122
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the disjoint (0,N)-cells property for homogeneous ANRs
Autorzy:
Krupski, Paweł
Powiązania:
https://bibliotekanauki.pl/articles/967209.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
absolute neighborhood retract
generalized manifold
homogeneous space
disjoint cells property
$LC^n$-space
Opis:
A metric space (X,ϱ) satisfies the disjoint (0,n)-cells property provided for each point x ∈ X, any map f of the n-cell $B^{n}$ into X and for each ε > 0 there exist a point y ∈ X and a map $g:B^{n} → X$ such that ϱ(x,y) < ε, $\widehat{ϱ}(f,g) < ε$ and $y ∉ g(B^{n})$. It is proved that each homogeneous locally compact ANR of dimension >2 has the disjoint (0,2)-cells property. If dimX = n > 0, X has the disjoint (0,n-1)-cells property and X is a locally compact $LC^{n-1}$-space then local homologies satisfy $H_{k}(X,X-x) = 0$ for k < n and H_{n}(X,X-x) ≠ 0.
Źródło:
Colloquium Mathematicum; 1993, 66, 1; 77-84
0010-1354
Pojawia się w:
Colloquium Mathematicum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The converse of the Hölder inequality and its generalizations
Autorzy:
Matkowski, Janusz
Powiązania:
https://bibliotekanauki.pl/articles/1290537.pdf
Data publikacji:
1994
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
measure space
integrable step functions
conjugate functions
a converse of Hölder inequality
subadditive function
convex function
generalized Hölder-Minkowski inequality
Opis:
Let (Ω,Σ,μ) be a measure space with two sets A,B ∈ Σ such that 0 < μ (A) < 1 < μ (B) < ∞ and suppose that ϕ and ψ are arbitrary bijections of [0,∞) such that ϕ(0) = ψ(0) = 0. The main result says that if $ʃ_Ω xydμ ≤ ϕ^{-1} (\int_{Ω} ϕ∘x dμ) ψ^{-1} (\int_{Ω} ψ∘x dμ)$ for all μ-integrable nonnegative step functions x,y then ϕ and ψ must be conjugate power functions. If the measure space (Ω,Σ,μ) has one of the following properties: (a) μ (A) ≤ 1 for every A ∈ Σ of finite measure; (b) μ (A) ≥ 1 for every A ∈ Σ of positive measure, then there exist some broad classes of nonpower bijections ϕ and ψ such that the above inequality holds true. A general inequality which contains integral Hölder and Minkowski inequalities as very special cases is also given.
Źródło:
Studia Mathematica; 1994, 109, 2; 171-182
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Weighted integrability and L¹-convergence of multiple trigonometric series
Autorzy:
Chen, Chang-Pao
Powiązania:
https://bibliotekanauki.pl/articles/1291177.pdf
Data publikacji:
1994
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
multiple trigonometric series
rectangular partial sums
Cesàro means
weighted integrability
L¹-convergence
conditions of generalized bounded variation
Opis:
We prove that if $c_{jk} → 0$ as max(|j|,|k|) → ∞, and $∑_{|j|=0±}^∞ ∑_{|k|=0±}^∞ θ(|j|^⊤)ϑ(|k|^⊤)|Δ_{12}c_{jk}| < ∞$, then f(x,y)ϕ(x)ψ(y) ∈ L¹(T²) and $∬_{T²} |s_{mn}(x,y) - f(x,y)|·|ϕ(x)ψ(y)|dxdy → 0$ as min(m,n) → ∞, where f(x,y) is the limiting function of the rectangular partial sums $s_{mn}(x,y)$, (ϕ,θ) and (ψ,ϑ) are pairs of type I. A generalization of this result concerning L¹-convergence is also established. Extensions of these results to double series of orthogonal functions are also considered. These results can be extended to n-dimensional case. The aforementioned results generalize work of Balashov [1], Boas [2], Chen [3,4,5], Marzuq [9], Móricz [11], Móricz-Schipp-Wade [14], and Young [16].
Źródło:
Studia Mathematica; 1994, 108, 2; 177-190
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Bounded projections in weighted function spaces in a generalized unit disc
Autorzy:
Karapetyan, A.
Powiązania:
https://bibliotekanauki.pl/articles/1311367.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
generalized unit disc
holomorphic and pluriharmonic functions
weighted spaces
integral representations
bounded integral operators
Opis:
Let $M_{m,n}$ be the space of all complex m × n matrices. The generalized unit disc in $M_{m,n}$ is $R_{m,n} = {Z ∈ M_{m,n}: I^{(m)} - ZZ^\ast \text{ is positive definite} }$. Here $I^{(m)} ∈ M_{m,m}$ is the unit matrix. If 1 ≤ p < ∞ and α > -1, then $L_{α}^{p}(R_{m,n})$ is defined to be the space $L^p{R_{m,n}; [det(I^{(m)} - ZZ^\ast)]^α dμ_{m,n}(Z)}$, where $μ_{m,n}$ is the Lebesgue measure in $M_{m,n}$, and $H_α^p(R_{m,n}) ⊂ L_{α}^{p}(R_{m,n})$ is the subspace of holomorphic functions. In [8,9] M. M. Djrbashian and A. H. Karapetyan proved that, if $Reβ > (α+1)//p -1$ (for 1 < p < ∞) and Re β ≥ α (for p = 1), then $f(\mathcal{Z})= T_{m,n}^{β}(f)(\mathcal{Z}), \mathcal{Z} ∈ R_{m,n},$ where $T_{m,n}^{β}$ is the integral operator defined by (0.13)-(0.14). In the present paper, given 1 ≤ p < ∞, we find conditions on α and β for $T_{m,n}^{β}$ to be a bounded projection of $L_α^p(R_{m,n})$ onto $H_α^p(R_{m,n})$. Some applications of this result are given.
Źródło:
Annales Polonici Mathematici; 1995, 62, 3; 193-218
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Convergence in the generalized sense relative to Banach algebras of operators and in LMC-algebras
Autorzy:
Barnes, Bruce A.
Powiązania:
https://bibliotekanauki.pl/articles/1289118.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
convergence in the generalized sense
spectral theory
LMC-algebra
Opis:
The notion of convergence in the generalized sense of a sequence of closed operators is generalized to the situation where the closed operators involved are affiliated with a Banach algebra of operators. Also, the concept of convergence in the generalized sense is extended to the context of a LMC-algebra, where it applies to the spectral theory of the algebra.
Źródło:
Studia Mathematica; 1995, 115, 1; 87-103
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Double exponential integrability, Bessel potentials and embedding theorems
Autorzy:
Edmunds, David E.
Gurka, Petr
Opic, Bohumír
Powiązania:
https://bibliotekanauki.pl/articles/1289003.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Bessel potential
Riesz potential, generalized Lorentz-Zygmund spaces
exponential integrability
Hardy inequality
Orlicz spaces
Bessel potential spaces
Opis:
This paper is a continuation of [5] and provides necessary and sufficient conditions for double exponential integrability of the Bessel potential of functions from suitable (generalized) Lorentz-Zygmund spaces. These results are used to establish embedding theorems for Bessel potential spaces which extend Trudinger's result.
Źródło:
Studia Mathematica; 1995, 115, 2; 151-181
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Effective formulas for complex geodesics in generalized pseudoellipsoids with applications
Autorzy:
Zwonek, Włodzimierz
Powiązania:
https://bibliotekanauki.pl/articles/1311501.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
complex geodesics
generalized pseudoellipsoids
biholomorphic equivalence of ellipsoids
Opis:
We introduce a class of generalized pseudoellipsoids and we get formulas for their complex geodesics in the convex case. Using these formulas we get a description of automorphisms of the pseudoellipsoids. We also solve the problem of biholomorphic equivalence of convex complex ellipsoids without any sophisticated machinery.
Źródło:
Annales Polonici Mathematici; 1995, 61, 3; 261-294
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Necessary and sufficient conditions for generalized convexity
Autorzy:
Krzyszkowski, Janusz
Powiązania:
https://bibliotekanauki.pl/articles/1311583.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
generalized convexity
unrestricted n-parameter family
Opis:
We give some necessary and sufficient conditions for an n-1 times differentiable function to be a generalized convex function with respect to an unrestricted n-parameter family.
Źródło:
Annales Polonici Mathematici; 1995, 61, 1; 77-88
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stronger bounds for generalized degrees and Menger path systems
Autorzy:
Faudree, R.
Tuza, Zs.
Powiązania:
https://bibliotekanauki.pl/articles/972047.pdf
Data publikacji:
1995
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
generalized degree
Menger
Opis:
For positive integers d and m, let $P_{d,m}(G)$ denote the property that between each pair of vertices of the graph G, there are m internally vertex disjoint paths of length at most d. For a positive integer t a graph G satisfies the minimum generalized degree condition δₜ(G) ≥ s if the cardinality of the union of the neighborhoods of each set of t vertices of G is at least s. Generalized degree conditions that ensure that $P_{d,m}(G)$ is satisfied have been investigated. In particular, it has been shown, for fixed positive integers t ≥ 5, d ≥ 5t², and m, that if an m-connected graph G of order n satisfies the generalized degree condition δₜ(G) > (t/(t+1))(5n/(d+2))+(m-1)d+3t², then for n sufficiently large G has property $P_{d,m}(G)$. In this note, this result will be improved by obtaining corresponding results on property $P_{d,m}(G)$ using a generalized degree condition δₜ(G), except that the restriction d ≥ 5t² will be replaced by the weaker restriction d ≥ max{5t+28,t+77}. Also, it will be shown, just as in the original result, that if the order of magnitude of δₜ(G) is decreased, then $P_{d,m}(G)$ will not, in general, hold; so the result is sharp in terms of the order of magnitude of δₜ(G).
Źródło:
Discussiones Mathematicae Graph Theory; 1995, 15, 2; 167-177
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 484

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