共查询到20条相似文献,搜索用时 31 毫秒
1.
Julio Delgado 《Integral Equations and Operator Theory》2010,68(1):61-74
Let Ω be a second countable topological space and μ be a σ−finite measure on the Borel sets M{\mathcal{M}}. Let T be a nuclear operator on Lp(W,M,m){L^p({\Omega},{\mathcal{M}},\mu) }, 1 < p < ∞, in this work we establish a formula for the trace of T. A preliminary trace formula is established applying the general theory of traces on operator ideals introduced by Pietsch
and a characterization of nuclear operators for σ−finite measures. We also use the Doob’s maximal theorem for martingales with the purpose of studying the kernel k(x, y) of T on the diagonal. 相似文献
2.
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
3.
Damir Z. Arov Mikael Kurula Olof J. Staffans 《Complex Analysis and Operator Theory》2011,5(2):331-402
This work is devoted to the construction of canonical passive and conservative state/signal shift realizations of arbitrary
passive continuous time behaviors. By definition, a passive future continuous time behavior is a maximal nonnegative right-shift
invariant subspace of the Kreĭn space L2([0,¥);W){L^2([0,\infty);\mathcal W)}, where W{\mathcal W} is a Kreĭn space, and the inner product in L2([0,¥);W){L^2([0,\infty);\mathcal W)} is the one inherited from W{\mathcal W}. A state/signal system S = (V;X,W){\Sigma=(V;\mathcal X,\mathcal W)}, with a Hilbert state space X{\mathcal X} and a Kreĭn signal space W{\mathcal W}, is a dynamical system whose classical trajectories (x, w) on [0, ∞) satisfy x ? C1([0,¥);X){x\in C^1([0,\infty);\mathcal X)}, w ? C([0,¥);W){w \in C([0,\infty);\mathcal W)}, and
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