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Gaussian processes

100%

Ciesielski Z.

Commentationes Mathematicae

|

1965

|

tom 9

|

nr 2

EN

The article contains no abstract

2

O pewnych nierównościach

100%

Ciesielski Z.

Commentationes Mathematicae

|

1956

|

tom 2

|

nr 2

EN

The article contains no abstract

3

On the spectrum of the Laplace operator

100%

Ciesielski Z.

Commentationes Mathematicae

|

1970

|

tom 14

|

nr 1

EN

The article contains no abstract

4

Fractal functions and Schauder bases

100%

Ciesielski Z.

Banach Center Publications

|

1995

|

tom 34

|

nr 1

47-54

5

The Lebesgue constants for the Franklin orthogonal system

64%

Ciesielski Z., Kamont A.

Studia Mathematica

|

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.

6

Przegląd niektórych nowszych metod w teorii potencjału, III

64%

Ciesielski Z., Semadeni Z.

Commentationes Mathematicae

|

1968

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tom 11

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nr 1

EN

The article contains no abstract

7

Gebelein's inequality and its consequences

64%

Beśka M., Ciesielski Z.

Banach Center Publications

|

2006

|

tom 72

|

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.

8

Przegląd niektórych nowszych metod w teorii potencjału, I

64%

Ciesielski Z., Semadeni Z.

Commentationes Mathematicae

|

1964

|

tom 8

|

nr 2

EN

The article contains no abstract

9

Quelques espaces fonctionnels associés à des processus gaussiens

52%

Ciesielski Z., Kerkyacharian G., Roynette B.

Studia Mathematica

|

1993

|

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

Probabilistic and analytic formulas for the periodic splines interpolating with multiple nodes

50%

Ciesielski Z.

Banach Center Publications

|

1979

|

tom 5

|

nr 1

35-45

11

Numerical integration with weights of convex functions of algebraic polynomials

50%

Ciesielski Z.

Colloquium Mathematicum

|

1990

|

tom 60-61

|

nr 2

671-679

12

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

13

The degenerate B-splines as a basis in the space of algebraic polynomials

45%

Ciesielski Z., Domsta J.

Annales Polonici Mathematici

|

1985

|

tom 46

|

nr 1

71-79

14

Equivalence of Haar and Franklin bases in $L_{p}$ spaces

39%

Ciesielski Z., Simon P., Sjölin P.

Studia Mathematica

|

1977

|

tom 60

|

nr 2

195-210

15

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

16

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

17

Estimates for spline orthonormal functions and for their derivatives

38%

Ciesielski Z., Domsta J.

Studia Mathematica

|

1972

|

tom 44

|

nr 4

315-320

18

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

19

Some properties of convex functions of higher orders

38%

Ciesielski Z.

Annales Polonici Mathematici

|

1959-1960

|

tom 7

|

nr 1

1-7

20

On absolute convergence of Haar series

32%

Ciesielski Z., Musielak J.

Colloquium Mathematicum

|

1959-1960

|

tom 7

|

nr 1

61-65

Ograniczanie wyników

Gaussian processes

O pewnych nierównościach

On the spectrum of the Laplace operator

Fractal functions and Schauder bases

The Lebesgue constants for the Franklin orthogonal system

Przegląd niektórych nowszych metod w teorii potencjału, III

Gebelein's inequality and its consequences

Przegląd niektórych nowszych metod w teorii potencjału, I

Quelques espaces fonctionnels associés à des processus gaussiens

Probabilistic and analytic formulas for the periodic splines interpolating with multiple nodes

Numerical integration with weights of convex functions of algebraic polynomials

Equivalence, unconditionality and convergence a.e. of the spline bases in $L_p$ spaces

The degenerate B-splines as a basis in the space of algebraic polynomials

Equivalence of Haar and Franklin bases in $L_{p}$ spaces

Construction of an orthonormal basis in $C^{m}(I^{d})$ and $W^{m}_{p}(I^{d})$

Spline bases in classical function spaces on compact $C^{∞}$ manifolds, Part II

Estimates for spline orthonormal functions and for their derivatives

Spline bases in classical function spaces on compact $C^{∞}$ manifolds, Part I

Some properties of convex functions of higher orders

On absolute convergence of Haar series