Autor: Bressan, Alberto - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Artykuł

Skocz do pozycji: 2.

Tytuł:: Selections and representations of multifunctions in paracompact spaces
Autorzy:: Bressan, Alberto
Colombo, Giovanni
Powiązania:: https://bibliotekanauki.pl/articles/1293156.pdf
Data publikacji:: 1992
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: directionally continuous selections
Opis:: Let (X,T) be a paracompact space, Y a complete metric space, $F:X → 2^Y$ a lower semicontinuous multifunction with nonempty closed values. We prove that if $T^+$ is a (stronger than T) topology on X satisfying a compatibility property, then F admits a $T^+$-continuous selection. If Y is separable, then there exists a sequence $(f_n)$ of $T^+$-continuous selections such that $F(x)=\overline{{f_n(x);n ≥ 1}}$ for all x ∈ X. Given a Banach space E, the above result is then used to construct directionally continuous selections on arbitrary subsets of ℝ × E.
Źródło:: Studia Mathematica; 1992, 102, 3; 209-216
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: A multidimensional Lyapunov type theorem
Autorzy:: Bressan, Alberto
Powiązania:: https://bibliotekanauki.pl/articles/1292599.pdf
Data publikacji:: 1993
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:: Given functions $f_1,...,f_ν ∈ ℒ^1(ℝ^n;ℝ^m)$, weights $p_1,...,p_ν: ℝ^n → [0,1]$ with $∑ p_i ≡ 1$, and any finite set of vectors $v_1,...,v_k ∈ ℝ^n ∖ {0}$, we prove the existence of a partition ${A_1,...,A_ν}$ of $ℝ^n$ such that the two functions $f_p = ∑_{i=1}^ν p_i f_i, $f_A = ∑_{i=1}^ν χ_{A_i}f_i$ have the same integral not only over $ℝ^n$, but also over every single line $x' + ℝv_j$, for each j = 1,...,k and almost every x' in the orthogonal hyperplane $v_j^⊥$. Equivalently, the Fourier transforms of $f_p$, $f_A$ satisfy $f̂_p(y) = f̂_A(y)$ for every $y ∈ ⋃ v_j^⊥$.
Źródło:: Studia Mathematica; 1993, 106, 2; 121-128
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: Extremal selections of multifunctions generating a continuous flow
Autorzy:: Bressan, Alberto
Crasta, Graziano
Powiązania:: https://bibliotekanauki.pl/articles/1311646.pdf
Data publikacji:: 1994
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: differential inclusion
extremal selection
Opis:: Let $F:[0,T] × ℝ^n → 2^{ℝ^n}$ be a continuous multifunction with compact, not necessarily convex values. In this paper, we prove that, if F satisfies the following Lipschitz Selection Property: (LSP) For every t,x, every y ∈ c̅o̅F(t,x) and ε > 0, there exists a Lipschitz selection ϕ of c̅o̅F, defined on a neighborhood of (t,x), with |ϕ(t,x)-y| < ε, then there exists a measurable selection f of ext F such that, for every x₀, the Cauchy problem ẋ(t) = f(t,x(t)), x(0) = x₀, has a unique Carathéodory solution, depending continuously on x₀. We remark that every Lipschitz multifunction with compact values satisfies (LSP). Another interesting class for which (LSP) holds consists of those continuous multifunctions F whose values are compact and have convex closure with nonempty interior.
Źródło:: Annales Polonici Mathematici; 1994-1995, 60, 2; 101-117
0066-2216
Pojawia się w:: Annales Polonici Mathematici
Dostawca treści:: Biblioteka Nauki

Artykuł

Informacja