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1
Content available remote Fractal functions and Schauder bases
100%
Ciesielski Z.
|
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nr 1
47-54
2
Content available On the spectrum of the Laplace operator
75%
Ciesielski Z.
|
|
nr 1
EN
The article contains no abstract
3
Content available remote The Lebesgue constants for the Franklin orthogonal system
63%
Ciesielski Z. , Kamont A.
Studia Mathematica
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2004
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tom 164
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nr 1
55-73
EN
To each set of knots $t_{i} = i/2n$ for i = 0,...,2ν and $t_{i} = (i-ν)/n$ for i = 2ν + 1,..., n + ν, with 1 ≤ ν ≤ n, there corresponds the space $𝓢_{ν,n}$ of all piecewise linear and continuous functions on I = [0,1] with knots $t_{i}$ and the orthogonal projection $P_{ν,n}$ of L²(I) onto $𝓢_{ν,n}$. The main result is $lim_{(n-ν)∧ ν → ∞} ||P_{ν,n}||₁ = sup_{ν,n : 1 ≤ ν ≤ n} ||P_{ν,n}||₁ = 2 + (2 - √3)²$. This shows that the Lebesgue constant for the Franklin orthogonal system is 2 + (2-√3)².
4
Content available remote Gebelein's inequality and its consequences
63%
Beśka M. , Ciesielski Z.
Banach Center Publications
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2006
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tom 72
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nr 1
11-23
EN
Let $(X_i, i=1,2,...)$ be the normalized gaussian system such that $X_i ∈ N(0,1)$, i = 1,2,... and let the correlation matrix $ρ_{ij} = E(X_iX_j)$ satisfy the following hypothesis: $C = sup_{i≥1} ∑_{j=1}^{∞} |ρ_{i,j}| < ∞$. We present Gebelein's inequality and some of its consequences: Borel-Cantelli type lemma, iterated log law, Levy's norm for the gaussian sequence etc. The main result is that (f(X₁) + ⋯ + f(Xₙ))/n → 0 a.s. for f ∈ L¹(ν) with (f,1)_ν = 0.
5
Content available Przegląd niektórych nowszych metod w teorii potencjału, I
63%
Ciesielski Z. , Semadeni Z.
Commentationes Mathematicae
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1964
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tom 8
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nr 2
EN
The article contains no abstract
6
Content available Przegląd niektórych nowszych metod w teorii potencjału, III
63%
Ciesielski Z. , Semadeni Z.
Commentationes Mathematicae
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1968
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tom 11
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nr 1
EN
The article contains no abstract
7
Content available Gaussian processes
63%
Ciesielski Z.
|
|
tom 9
|
nr 2
EN
The article contains no abstract
8
Content available O pewnych nierównościach
63%
Ciesielski Z.
|
|
tom 2
|
nr 2
EN
The article contains no abstract
9
Content available remote Quelques espaces fonctionnels associés à des processus gaussiens
51%
Ciesielski Z. , Kerkyacharian G. , Roynette B.
|
|
tom 107
|
nr 2
171-204
EN
The first part of the paper presents results on Gaussian measures supported by general Banach sequence spaces and by particular spaces of Besov-Orlicz type. In the second part, a new constructive isomorphism between the just mentioned sequence spaces and corresponding function spaces is established. Consequently, some results on the support function spaces for the Gaussian measure corresponding to the fractional Brownian motion are proved. Next, an application to stochastic equations is given. The last part of the paper contains a result on the support function spaces for stable processes with independent increments.
10
Content available remote Equivalence, unconditionality and convergence a.e. of the spline bases in $L_p$ spaces
50%
Ciesielski Z.
Banach Center Publications
|
1979
|
tom 4
|
nr 1
55-68
11
Content available The degenerate B-splines as a basis in the space of algebraic polynomials
44%
Ciesielski Z. , Domsta J.
|
1985
|
tom 46
|
nr 1
71-79
12
Content available remote Equivalence of Haar and Franklin bases in $L_{p}$ spaces
38%
Ciesielski Z. , Simon P. , Sjölin P.
|
|
nr 2
195-210
13
Content available remote Spline bases in classical function spaces on compact $C^{∞}$ manifolds, Part I
38%
Ciesielski Z. , Figiel T.
Studia Mathematica
|
1983
|
tom 76
|
nr 1
1-58
14
Content available remote Construction of an orthonormal basis in $C^{m}(I^{d})$ and $W^{m}_{p}(I^{d})$
38%
Ciesielski Z. , Domsta J.
Studia Mathematica
|
1972
|
tom 41
|
nr 2
211-224
15
Content available remote Spline bases in classical function spaces on compact $C^{∞}$ manifolds, Part II
38%
Ciesielski Z. , Figiel T.
Studia Mathematica
|
1983
|
tom 76
|
nr 2
95-136
16
Content available remote Some properties of convex functions of higher orders
38%
Ciesielski Z.
|
|
tom 7
|
nr 1
1-7
17
Content available remote A note on a selection problem
32%
Ciesielski Z. , Zabczyk J.
Banach Center Publications
|
1979
|
tom 5
|
nr 1
47-51
18
Content available remote Properties of the orthonormal Franklin system
32%
Ciesielski Z.
Studia Mathematica
|
1963-1964
|
tom 23
|
nr 2
141-157
19
Content available Fourier analysis of the Banach indicatrix
32%
Ciesielski Z.
|
1966
|
tom 15
|
nr 1
99-103
20
Content available remote A construction of basis in $C^{(1)}(I^{2})$
32%
Ciesielski Z.
|
|
nr 2
243-247
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