Let U be an invertible operator on a Banach space Y. U is said to be trigonometrically well-bounded provided the sequence {U n } n ∞ =∞ is the Fourier-Stieltjes transform of a suitable projection-valued funct
We are interested in the question whether the-semigroup converges to 0 with respect to the operator norm as, i.e. whetheras. In this case,for someand all, so the semigroup is said to beuniformly exponentially stable. A necessary condition for the uniform exponential stability of a-semigrou...
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A linear map from Rn to Rm can be expressed in terms of an m×n matrix A: A[x1x2⋮xn]∈Rm A linear map A has two important properties: A(v+w)=A(v)+A(w) for v,w∈Rn A(cv)=cA(v) for v∈Rn and...
An n × n-matrix-valued function A(t) on T is called regressive if I + µ(t)A(t) is invertible for all t ∈ T. The set of functions being both regressive and rd-continuous is denoted by R = R(T) = R(T, R)(R(T, R n×n )). The set of all regressive functions ...
There are also other criteria for exponential dichotomy in terms of the existence of solutions of inhomogeneous equations in certain spaces (Massera and Schäffer [5], Coppel [2]) or in terms of the existence of a Lyapunov function (Coppel [2]) but these ...
The mixing system is supposed to be stable and invertible and the input signals, also called sources, are assumed zero-mean independent and identically distributed (IID) random signals. Using the hypothesis that sources are statistically independent, we propose a generalization to the convolutive case...
a utility function\(u_{i}:A_{1}\times \dots \times A_{n}\times \Omega \rightarrow \mathbb {R}\); for each\(\lambda \in \Lambda \), a probability distribution\(P_{\lambda }\)over\(\Omega \). Apolicyof playeriin such a game is a function\(\sigma _{i}:T_{i}\times ...
In fact, this decomposition can always be done in a way that controls the norms of y and z: If the cone X + is generating, then there exists a number M > 0 with the following property: for each x ∈ X there exist y, z ∈ X + such that x = y − z and y , z ≤ M ...
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