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1.
Let X be a Banach space with a separable dual X*. Let ${Y\subset X}Let X be a Banach space with a separable dual X*. Let Y ì X{Y\subset X} be a closed subspace, and
f:Y?\mathbbR{f:Y\rightarrow\mathbb{R}} a C
1-smooth function. Then we show there is a C
1 extension of f to X. 相似文献
2.
The main result is that, for any projective compact analytic subset Y of dimension q > 0 in a reduced complex space X, there is a neighborhood Ω of Y such that, for any covering space ${\Upsilon\colon\widehat X\to X}The main result is that, for any projective compact analytic subset Y of dimension q > 0 in a reduced complex space X, there is a neighborhood Ω of Y such that, for any covering space
U\colon[^(X)]? X{\Upsilon\colon\widehat X\to X} in which [^(Y)] o U-1(Y){\widehat Y\equiv\Upsilon^{-1}(Y)} has no noncompact connected analytic subsets of pure dimension q with only compact irreducible components, there exists a C
∞ exhaustion function j{\varphi} on [^(X)]{\widehat X} which is strongly q-convex on [^(W)]=U-1(W){\widehat\Omega=\Upsilon^{-1}(\Omega)} outside a uniform neighborhood of the q-dimensional compact irreducible components of [^(Y)]{\widehat Y}. 相似文献
3.
Daniela Roşu 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(4):479-496
In this paper we consider a nonlinear evolution reaction–diffusion system governed by multi-valued perturbations of m-dissipative operators, generators of nonlinear semigroups of contractions. Let X and Y be real Banach spaces, ${\mathcal{K}}In this paper we consider a nonlinear evolution reaction–diffusion system governed by multi-valued perturbations of m-dissipative operators, generators of nonlinear semigroups of contractions. Let X and Y be real Banach spaces, K{\mathcal{K}} be a nonempty and locally closed subset in
\mathbbR ×X×Y, A:D(A) í X\rightsquigarrow X, B:D(B) í Y\rightsquigarrow Y{\mathbb{R} \times X\times Y,\, A:D(A)\subseteq X\rightsquigarrow X, B:D(B)\subseteq Y\rightsquigarrow Y} two m-dissipative operators, F:K ? X{F:\mathcal{K} \rightarrow X} a continuous function and
G:K \rightsquigarrow Y{G:\mathcal{K} \rightsquigarrow Y} a nonempty, convex and closed valued, strongly-weakly upper semi-continuous (u.s.c.) multi-function. We prove a necessary
and a sufficient condition in order that for each (t,x,h) ? K{(\tau,\xi,\eta)\in \mathcal{K}}, the next system
{ lc u¢(t) ? Au(t)+F(t,u(t),v(t)) t 3 tv¢(t) ? Bv(t)+G(t,u(t),v(t)) t 3 tu(t)=x, v(t)=h, \left\{ \begin{array}{lc} u'(t)\in Au(t)+F(t,u(t),v(t))\quad t\geq\tau \\ v'(t)\in Bv(t)+G(t,u(t),v(t))\quad t\geq\tau \\ u(\tau)=\xi,\quad v(\tau)=\eta, \end{array} \right. 相似文献
4.
Rafael Dahmen 《Mathematische Zeitschrift》2010,266(1):115-140
We give a sufficient criterion for complex analyticity of nonlinear maps defined on direct limits of normed spaces. This tool is then used to construct new classes of (real and complex) infinite dimensional Lie groups: The group DiffGerm (K, X) of germs of analytic diffeomorphisms around a compact set K in a Banach space X and the group ${\bigcup_{n\in\mathbb {N}}G_n}
5.
We show that if an infinite-dimensional Banach space X has a symmetric basis then there exists a bounded, linear operator ${R\,:\,X\longrightarrow\, X}
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