K. Dziedziul

activity

20182023

most citedMultiresolution analysis and adaptive estimation on a sphere using stereographic wavelets

1 citations · 2 across the 6 of their papers we have counts for

collaborators

8 papers

cs.LG2023

Mercer Large-Scale Kernel Machines from Ridge Function Perspective

Karol Dziedziul, Sergey Kryzhevich, Paweł Wieczyński

To present Mercer large-scale kernel machines from a ridge function perspective, we recall the results by Lin and Pinkus from {\it Fundamentality of ridge functions}. We consider t…

math.CA2021

Marcinkiewicz averages of smooth orthogonal projections on sphere

Marcin Bownik, Karol Dziedziul, Anna Kamont

We construct a single smooth orthogonal projection with desired localization whose average under a group action yields the decomposition of the identity operator. For any full rank…

math.FA2020

Parseval wavelet frames on Riemannian manifold

Marcin Bownik, Karol Dziedziul, Anna Kamont

We construct Parseval wavelet frames in $L^{2} (M)$ for a general Riemannian manifold $M$ and we show the existence of wavelet unconditional frames in $L^{p} (M)$ for $1 < p < \infty$ . Th…

math.CA2018

Box-splines orthogonal projections

M. Beśka, K. Dziedziul

Let $P$ be orthogonal projection on B-splines of degree $r - 1$ with equally spaced knots. Sweldens and Piessens proved that $P (x^{r}) - x^{r}$ is Bernoulli polynomial. We generalize Sweld…

math.ST2018

Note on universal algorithms for learning theory

Karol Dziedziul, Barbara Wolnik

We propose the general way of study the universal estimator for the regression problem in learning theory considered in "Universal algorithms for learning theory Part I: piecewise…

math.ST2018★ 1 cited

Multiresolution analysis and adaptive estimation on a sphere using stereographic wavelets

Bogdan Ćmiel, Karol Dziedziul, Natalia Jarzębkowska

We construct an adaptive estimator of a density function on $d$ dimensional unit sphere $S^{d}$ ( $d \geq 2$ ), using a new type of spherical frames. The frames, or as we call them, s…

math.ST2018★ 1 cited

The smoothness test for a density function

Bogdan Ćmiel, Karol Dziedziul, Barbara Wolnik

The problem of testing hypothesis that a density function has no more than $μ$ derivatives versus it has more than $μ$ derivatives is considered. For a solution, the $L^{2}$ norms of…

math.CA2018

Smooth orthogonal projections on Riemannian manifold

Marcin Bownik, Karol Dziedziul, Anna Kamont

We construct a decomposition of the identity operator on a Riemannian manifold $M$ as a sum of smooth orthogonal projections subordinate to an open cover of $M$ . This extends a dec…