DSpace Repository :: Browsing by Author "Wronicz, Zygmunt"

Thesis

Restricted

Bazy w przestrzeniach Banacha

(Data obrony: 2013-09-25) Szlęk, Magdalena
Wydział Matematyki Stosowanej

Thesis

Restricted

Falki o nośniku zwartym

(Data obrony: 2014-10-30) Nikiel, Paweł
Wydział Matematyki Stosowanej

Thesis

Restricted

Falkowe estymatory funkcji gęstości i funkcji regresji

(Data obrony: 2013-10-23) Gomułka, Magdalena
Wydział Matematyki Stosowanej

Thesis

Restricted

Funkcje kwaternionowe

(Data obrony: 2009-09-23) Suder, Marcin
Wydział Matematyki Stosowanej

Thesis

Restricted

Interpolacja naturalnymi funkcjami giętymi - definicja i zastosowanie

(Data obrony: 2012-10-18) Kochański, Wojciech
Wydział Matematyki Stosowanej

Thesis

Restricted

Najlepsza koaproksymacja w przestrzeniach liniowych unormowanych

(Data obrony: 2013-12-19) Wilczek, Barbara
Wydział Matematyki Stosowanej

Article

Open Access

On a problem of Gevorkyan for the Franklin system

(2016) Wronicz, Zygmunt

In 1870 G. Cantor proved that if $\lim_{N\rightarrow\infty}\sum_{n=-N}^N\,c_{n}e^{inx} = 0$ for every real $x$, where $\bar{c}_{n}=c_{n}$ $n\in \mathbb{Z}$, then all coefficients $c$ are equal to zero. Later, in 1950 V.Ya. Kozlov proved that there exists a trigonometric series for which a subsequence of its partial sums converges to zero, where not all coefficients of the series are zero. In 2004 G. Gevorkyan raised the issue that if Cantor's result extends to the Franklin system. The conjecture remains open until now. In the present paper we show however that Kozlov's version remains true for Franklin's system.

Article

Open Access

On some application of biorthogonal spline systems to integral equations

(2005) Wronicz, Zygmunt

We consider an operator $P_N: L_p(I) \to S_n(\Delta_N)$, such that $P_Nf=f$ for $f\in S_n(\Delta_N)$, where $S_n(\Delta_N)$ is the space of splines of degree $n$ with respect to a given partition $\Delta_N$ of the interval $I$. This operator is defined by means of a system of step functions biorthogonal to $B$-splines. Then we use this operator to approximation to the solution of the Fredholm integral equation of the second kind. Convergence rates for the approximation of the solution of this equation are given.

Thesis

Metadata only

Rozkłady atomowe w przestrzeniach Banacha

(Data obrony: 2013-07-16) Skiba, Piotr
Wydział Matematyki Stosowanej

Thesis

Restricted

Twierdzenie Charsziładze-Łozińskiego

(Data obrony: 2012-10-18) Brzyska, Marta
Wydział Matematyki Stosowanej

Article

Open Access

Uniqueness of series in the Franklin system and the Gevorkyan problems

(Wydawnictwa AGH, 2021) Wronicz, Zygmunt

In 1870 G. Cantor proved that if $\lim_{N \rightarrow \infty}\sum_{n=-N}^N c_{n}e^{inx} = 0$, $\bar{c}_{n}=c_{n}$, then $c_{n}=0$ for $n \in \mathbb{Z}$. In 2004 G. Gevorkyan raised the issue that if Cantor's result extends to the Franklin system. He solved this conjecture in 2015. In 2014 Z. Wronicz proved that there exists a Franklin series for which a subsequence of its partial sums converges to zero, where not all coefficients of the series are zero. In the present paper we show that to the uniqueness of the Franklin system $\lim_{n\rightarrow \infty}\sum_{n=0}^\infty a_{n}f_{n}$ it suffices to prove the convergence its subsequence $s_{2^{n}}$ to zero by the condition $a_{n}=o(\sqrt{n})$. It is a solution of the Gevorkyan problem formulated in 2016.