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Wyświetlanie 1-15 z 18
Tytuł:
On the $L_1$-convergence of Fourier series
Autorzy:
Fridli, S.
Powiązania:
https://bibliotekanauki.pl/articles/1219140.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Fourier series
$L_1$-convergence
a.e. convergence
Opis:
Since the trigonometric Fourier series of an integrable function does not necessarily converge to the function in the mean, several additional conditions have been devised to guarantee the convergence. For instance, sufficient conditions can be constructed by using the Fourier coefficients or the integral modulus of the corresponding function. In this paper we give a Hardy-Karamata type Tauberian condition on the Fourier coefficients and prove that it implies the convergence of the Fourier series in integral norm, almost everywhere, and if the function itself is in the real Hardy space, then also in the Hardy norm. We also compare it to the previously known conditions.
Źródło:
Studia Mathematica; 1997, 125, 2; 161-174
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Convergence in nonisotropic regions of harmonic functions in $^n$
Autorzy:
Cascante, Carme
Ortega, Joaquin
Powiązania:
https://bibliotekanauki.pl/articles/1217595.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
harmonic and holomorphic functions
tangential convergence
Opis:
We study the boundedness in $L^p(^n)$ of the projections onto spaces of functions with spectrum contained in horizontal strips. We obtain some results concerning convergence along nonisotropic regions of harmonic extensions of functions in $L^p(^n)$ with spectrum included in these horizontal strips.
Źródło:
Studia Mathematica; 1999, 134, 3; 269-298
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Summable families in nuclear groups
Autorzy:
Banaszczyk, Wojciech
Powiązania:
https://bibliotekanauki.pl/articles/1292681.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
nuclear groups
unconditional and absolute convergence
Opis:
Nuclear groups form a class of abelian topological groups which contains LCA groups and nuclear locally convex spaces, and is closed with respect to certain natural operations. In nuclear locally convex spaces, weakly summable families are strongly summable, and strongly summable are absolutely summable. It is shown that these theorems can be generalized in a natural way to nuclear groups.
Źródło:
Studia Mathematica; 1993, 105, 3; 271-282
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Unconditional ideals in Banach spaces
Autorzy:
Godefroy, G.
Kalton, N.
Saphar, P.
Powiązania:
https://bibliotekanauki.pl/articles/1292973.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
M-ideal
hermitian operator
unconditional convergence
Opis:
We show that a Banach space with separable dual can be renormed to satisfy hereditarily an "almost" optimal uniform smoothness condition. The optimal condition occurs when the canonical decomposition $X*** = X^{⊥} ⊕ X*$ is unconditional. Motivated by this result, we define a subspace X of a Banach space Y to be an h-ideal (resp. a u-ideal) if there is an hermitian projection P (resp. a projection P with ∥I-2P∥ = 1) on Y* with kernel $X^{⊥}$. We undertake a general study of h-ideals and u-ideals. For example we show that if a separable Banach space X is an h-ideal in X** then X has the complex form of Pełczyński's property (u) with constant one and the Baire-one functions Ba(X) in X** are complemented by an hermitian projection; the converse holds under a compatibility condition which is shown to be necessary. We relate these ideas to the more familiar notion of an M-ideal, and to Banach lattices. We further investigate when, for a separable Banach space X, the ideal of compact operators K(X) is a u-ideal or an h-ideal in ℒ(X) or K(X)**. For example, we show that K(X) is an h-ideal in K(X)** if and only if X has the "unconditional compact approximation property" and X is an M-ideal in X**.
Źródło:
Studia Mathematica; 1993, 104, 1; 13-59
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
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:
Almost everywhere summability of Laguerre series. II
Autorzy:
Stempak, K.
Powiązania:
https://bibliotekanauki.pl/articles/1293043.pdf
Data publikacji:
1992
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Laguerre expansions
Cesàro means
almost everywhere convergence
Opis:
Using methods from [9] we prove the almost everywhere convergence of the Cesàro means of Laguerre series associated with the system of Laguerre functions $L^a_n(x) = (n!/Γ(n+a+1))^{1/2} e^{-x/2} x^{a/2} L_n^a(x)$, n = 0,1,2,..., a ≥ 0. The novel ingredient we add to our previous technique is the $A_p$ weights theory. We also take the opportunity to comment and slightly improve on our results from [9].
Źródło:
Studia Mathematica; 1992, 103, 3; 317-327
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An inverse Sidon type inequality
Autorzy:
Fridli, S.
Powiązania:
https://bibliotekanauki.pl/articles/1292682.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Sidon type inequalities
Hardy spaces
convergence classes
Opis:
Sidon proved the inequality named after him in 1939. It is an upper estimate for the integral norm of a linear combination of trigonometric Dirichlet kernels expressed in terms of the coefficients. Since the estimate has many applications for instance in $L^1$ convergence problems and summation methods with respect to trigonometric series, newer and newer improvements of the original inequality has been proved by several authors. Most of them are invariant with respect to the rearrangement of the coefficients. Although the newest results are close to best possible, no nontrivial lower estimate has been given so far. The aim of this paper is to give the best rearrangement invariant function of coefficients that can be used in a Sidon type inequality. We also show that it is equivalent to an Orlicz type and a Hardy type norm. Examples of applications are also given.
Źródło:
Studia Mathematica; 1993, 105, 3; 283-308
0039-3223
Pojawia się w:
Studia Mathematica
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:
Almost everywhere convergence of Laguerre series
Autorzy:
Chen, Chang-Pao
Lin, Chin-Cheng
Powiązania:
https://bibliotekanauki.pl/articles/1290468.pdf
Data publikacji:
1994
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
almost everywhere convergence
Cesàro means
Laguerre polynomials
Riesz means
Opis:
Let $a ∈ ℤ^+$ and $f ∈ L^p (ℝ^+), 1 ≤ p ≤ ∞ $. Denote by $c_j$ the inner product of f and the Laguerre function $ℒ^a_j$. We prove that if ${c_j}$ satisfies $lim_{λ↓1} \overline lim_{n→∞} ∑_{n
Źródło:
Studia Mathematica; 1994, 109, 3; 291-301
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Lévy continuity theorem for nuclear groups
Autorzy:
Banaszczyk, W.
Powiązania:
https://bibliotekanauki.pl/articles/1216904.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Lévy continuity theorem
convergence of probability measures
nuclear groups
Opis:
Let G be an abelian topological group. The Lévy continuity theorem says that if G is an LCA group, then it has the following property (PL) a sequence of Radon probability measures on G is weakly convergent to a Radon probability measure μ if and only if the corresponding sequence of Fourier transforms is pointwise convergent to the Fourier transform of μ. Boulicaut [Bo] proved that every nuclear locally convex space G has the property (PL). In this paper we prove that the property (PL) is inherited by nuclear groups, a variety of abelian topological groups containing LCA groups and nuclear locally convex spaces, introduced in [B1].
Źródło:
Studia Mathematica; 1999, 136, 2; 183-196
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Ergodic theorems for subadditive superstationary families of random sets with values in Banach spaces
Autorzy:
Krupa, G.
Powiązania:
https://bibliotekanauki.pl/articles/1217806.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
multivalued ergodic theorems
measurable multifunctions
random sets
subadditive superstationary processes
set convergence
Opis:
Under different compactness assumptions pointwise and mean ergodic theorems for subadditive superstationary families of random sets whose values are weakly (or strongly) compact convex subsets of a separable Banach space are presented. The results generalize those of [14], where random sets in $ℝ^d$ are considered. Techniques used here are inspired by [3].
Źródło:
Studia Mathematica; 1998, 131, 3; 289-302
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Vector series whose lacunary subseries converge
Autorzy:
Drewnowski, Lech
Labuda, Iwo
Powiązania:
https://bibliotekanauki.pl/articles/1206244.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
subseries convergence
lacunary subseries
zero-density subseries
lacunary convergence property
topological Riesz space of measurable functions
topological vector space of Bochner measurable functions
Lebesgue property
Levi property
copy of $c_0$
Opis:
The area of research of this paper goes back to a 1930 result of H. Auerbach showing that a scalar series is (absolutely) convergent if all its zero-density subseries converge. A series $∑_n x_n$ in a topological vector space X is called ℒ-convergent if each of its lacunary subseries $∑_k x_{n_k}$ (i.e. those with $n_{k+1} - n_k → ∞$) converges. The space X is said to have the Lacunary Convergence Property, or LCP, if every ℒ-convergent series in X is convergent; in fact, it is then subseries convergent. The Zero-Density Convergence Property, or ZCP, is defined similarly though of lesser importance here. It is shown that for every ℒ-convergent series the set of all its finite sums is metrically bounded; however, it need not be topologically bounded. Next, a space with the LCP contains no copy of the space $c_0$. The converse holds for Banach spaces and, more generally, sequentially complete locally pseudoconvex spaces. However, an F-lattice of measurable functions is constructed that has both the Lebesgue and Levi properties, and thus contains no copy of $c_0$, and, nonetheless, lacks the LCP. The main (and most difficult) result of the paper is that if a Banach space E contains no copy of $c_0$ and λ is a finite measure, then the Bochner space $L_0$ (λ,e) has the LCP. From this, with the help of some Orlicz-Pettis type theorems proved earlier by the authors, the LCP is deduced for a vast class of spaces of (scalar and vector) measurable functions that have the Lebesgue type property and are "metrically-boundedly sequentially closed" in the containing $L_0$ space. Analogous results about the convergence of ℒ-convergent positive series in topological Riesz spaces are also obtained. Finally, while the LCP implies the ZCP trivially, an example is given that the converse is false, in general.
Źródło:
Studia Mathematica; 2000, 138, 1; 53-80
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Almost sure approximation of unbounded operators in $L_2 (X,A,μ)$
Autorzy:
Jajte, Ryszard
Paszkiewicz, Adam
Powiązania:
https://bibliotekanauki.pl/articles/1218552.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
$L_2(X,A,μ)$
unbounded operators
almost sure convergence
projections
unitary operators
approximation
Opis:
The possibilities of almost sure approximation of unbounded operators in $L_2(X,A,μ)$ by multiples of projections or unitary operators are examined.
Źródło:
Studia Mathematica; 1998, 128, 2; 103-120
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On convergence for the square root of the Poisson kernel in symmetric spaces of rank 1
Autorzy:
Rönning, Jan-Olav
Powiązania:
https://bibliotekanauki.pl/articles/1219076.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
maximal function
square root of the Poisson kernel
convergence region
symmetric space of rank 1
Opis:
Let P(z,β) be the Poisson kernel in the unit disk , and let $P_{λ}f(z) = ʃ_{∂} P(z,φ)^{1//2+λ} f(φ)dφ$ be the λ -Poisson integral of f, where $f ∈ L^p(∂)$. We let $P_{λ}f$ be the normalization $P_{λ}f//P_{λ}1$. If λ >0, we know that the best (regular) regions where $P_{λ}f$ converges to f for a.a. points on ∂ are of nontangential type. If λ =0 the situation is different. In a previous paper, we proved a result concerning the convergence of $P_0f$ toward f in an $L^p$ weakly tangential region, if $f ∈ L^p(∂)$ and p > 1. In the present paper we will extend the result to symmetric spaces X of rank 1. Let f be an $L^p$ function on the maximal distinguished boundary K/M of X. Then $P_{0}f(x)$ will converge to f(kM) as x tends to kM in an $L^p$ weakly tangential region, for a.a. kM ∈ K/M.
Źródło:
Studia Mathematica; 1997, 125, 3; 219-229
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
Wyświetlanie 1-15 z 18

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