Wyniki wyszukiwania

1

A multidimensional Lyapunov type theorem

100%

Bressan A.

Studia Mathematica

|

1993

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tom 106

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nr 2

121-128

EN

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 $y ∈ ⋃ v_j^⊥$.

2

Selections and representations of multifunctions in paracompact spaces

64%

Bressan A., Colombo G.

Studia Mathematica

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1992

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tom 102

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nr 3

209-216

EN

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.

3

Extremal selections of multifunctions generating a continuous flow

64%

Bressan A., Crasta G.

Annales Polonici Mathematici

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1994-1995

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tom 60

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nr 2

101-117

EN

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.

4

Extensions and selections of maps with decomposable values

45%

Bressan A., Colombo G.

Studia Mathematica

|

1988

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tom 90

|

nr 1

69-86

5

From optimal control to non-cooperative differential games: a homotopy approach

44%

Bressan A.

Control and Cybernetics

|

2009

|

tom 38

|

nr 4A

1081-1106

Ograniczanie wyników

3 Studia Mathematica

1 Annales Polonici Mathematici

1 Control and Cybernetics

5 Bressan A.

2 Colombo G.

1 Crasta G.

1 2009

1 1994

1 1993

1 1992

1 1988

A multidimensional Lyapunov type theorem

Selections and representations of multifunctions in paracompact spaces

Extremal selections of multifunctions generating a continuous flow

Extensions and selections of maps with decomposable values

From optimal control to non-cooperative differential games: a homotopy approach