Wyniki wyszukiwania

1

On some conjecture concerning Gaussian measures of dilatations of convex symmetric sets

100%

Kwapień S., Sawa J.

Studia Mathematica

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1993

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tom 105

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nr 2

173-187

EN

The paper deals with the following conjecture: if μ is a centered Gaussian measure on a Banach space F,λ > 1, K ⊂ F is a convex, symmetric, closed set, P ⊂ F is a symmetric strip, i.e. P = {x ∈ F : |x'(x)| ≤ 1} for some x' ∈ F', such that μ(K) = μ(P) then μ(λK) ≥ μ(λP). We prove that the conjecture is true under the additional assumption that K is "sufficiently symmetric" with respect to μ, in particular it is true when K is a ball in Hilbert space. As an application we give estimates of Gaussian measures of large and small balls in a Hilbert space.

2

On the Kaczmarz algorithm of approximation in infinite-dimensional spaces

100%

Kwapień S., Mycielski J.

Studia Mathematica

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2001

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tom 148

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nr 1

75-86

EN

The Kaczmarz algorithm of successive projections suggests the following concept. A sequence $(e_{k})$ of unit vectors in a Hilbert space is said to be effective if for each vector x in the space the sequence (xₙ) converges to x where (xₙ) is defined inductively: x₀ = 0 and $xₙ = x_{n-1} + αₙeₙ$, where $αₙ = ⟨x - x_{n-1},eₙ⟩$. We prove the effectivity of some sequences in Hilbert spaces. We generalize the concept of effectivity to sequences of vectors in Banach spaces and we prove some results for this more general concept.

3

Erratum to the paper "On the Kaczmarz algorithm of approximation in infinite-dimensional spaces" (Studia Math. 148 (2001), 75-86)

100%

Kwapień S., Mycielski J.

Studia Mathematica

|

2006

|

tom 176

|

nr 1

4

An estimation of the Lebesgue functions of biorthogonal systems with an application to the non-existence of some bases in C and $L^{1}$

100%

Kwapień S., Szarek S. J.

Studia Mathematica

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1979-1980

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tom 66

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nr 2

185-200

5

Some combinatorial and probabilistic inequalities and their application to Banach space theory II

80%

Kwapień S., Schütt C.

Studia Mathematica

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1989-1990

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tom 95

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nr 2

141-154

6

Some combinatorial and probabilistic inequalities and their application to Banach space theory

80%

Kwapień S., Schütt C.

Studia Mathematica

|

1985

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tom 82

|

nr 1

91-106

Ograniczanie wyników

6 Studia Mathematica

6 Kwapień S.

2 Mycielski J.

2 Schütt C.

1 Sawa J.

1 Szarek S. J.

1 2006

1 2001

1 1993

1 1989

1 1985

1 1979

On some conjecture concerning Gaussian measures of dilatations of convex symmetric sets

On the Kaczmarz algorithm of approximation in infinite-dimensional spaces

Erratum to the paper "On the Kaczmarz algorithm of approximation in infinite-dimensional spaces" (Studia Math. 148 (2001), 75-86)

An estimation of the Lebesgue functions of biorthogonal systems with an application to the non-existence of some bases in C and $L^{1}$

Some combinatorial and probabilistic inequalities and their application to Banach space theory II

Some combinatorial and probabilistic inequalities and their application to Banach space theory