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Schramm spaces and composition operators

Wróbel Małgorzata

Journal of Applied Mathematics and Computational Mechanics

2023

Vol. 22, nr 2

87--98

We give some properties of Schramm functions; among others, we prove that the family of all continuous piecewise linear functions defined on a real interval I is contained in the space ΦBV (I) of functions of bounded variation in the sense of Schramm. Moreover, we show that the generating function of the corresponding Nemytskij composition operator acting between Banach spaces CΦBV (I) of continuous functions of bounded Schramm variation has to be continuous and additionally we show that a space CΦBV (I) has the Matkowski property.

Operators with memory in Schramm spaces

Wróbel Małgorzata

Journal of Applied Mathematics and Computational Mechanics

2023

Vol. 22, nr 3

69--80

We show that every operator with memory acting between Banach spaces CΦBV(I) of continuous functions of bounded variation in the sense of Schramm defined on a compact interval I of a real axis, is a Nemytskij composition operator with the continuous generating function. Moreover, some consequences for uniformly bounded operators with memory will be given. As a by-product, we obtain that a Banach space CΦBV(I) has the uniform Matkowski property.

Locally defined operators acting C∞ (A) into C0 (A)

Wróbel Małgorzata

Journal of Applied Mathematics and Computational Mechanics

2022

Vol. 21, nr 2

103--110

We investigate the locally defined operators, sometimes called operators with memory, that map the space C∞ (A) of continuously differentiable functions in the sense of Whitney defined on a compact subset A ⊂ Rn into the space of continuous functions defined on the same set A. Using the Whitney Extension Theorem, we give a representation formula for such operators stating that every local operator K : C∞ (A) → C0 (A) is a generalized Nemytskii operator generated by some function h : A × RN → R.

Cyberprzestępczość w polskim systemie prawnym

Wróbel Małgorzata

Wiedza Obronna

2014

nr 4

72--90

W artykule zostały poruszone kwestie uregulowania zjawiska cyberprzestępczości w polskim systemie prawnym. Autorka ukazała aktualne problemy związane z uporządkowaniem legislacyjnym dotyczącym czynów zabronionych w cyberprzestrzeni oraz propozycje ich rozwiązania.

The article dealt with the issues of cybercrime legislation in the Polish legal system. The author presents the current problems associated with the ordering of legislation related to criminal acts in cyberspace as well as suggestions for their solution.