Currently displaying 1 – 9 of 9

Showing per page

Order by Relevance | Title | Year of publication

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

Stanisław KwapieńJerzy Sawa — 1993

Studia Mathematica

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...

On the Kaczmarz algorithm of approximation in infinite-dimensional spaces

Stanisław KwapieńJan Mycielski — 2001

Studia Mathematica

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 x = x n - 1 + α e , where α = x - x n - 1 , e . 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.

Page 1

Download Results (CSV)