where A is the infinitesimal generator of the C0-semigroup T (t) on the state space X, B is a bounded linear operator from input space U to X, C is a bounded linear operator from X to the output space Y , and D is a bounded operator from U to Y . The spaces X, U and Y are assumed to be Banach spaces. More detail on the system (1) can be found in Curtain and Zwart [1]. For the system (1) we intr...

We numerically solve parabolic problems in , , where is a bounded interval and is a strongly elliptic integrodifferential operator of order ! #" %$'& . A discontinuous Galerkin (dG) discretization in time and a wavelet discretization in space are used. The densely populated matrices in the corresponding linear systems of equations are replaced by sparse ones using appropriate wavelet compressio...

Let Ω be an open set in R (d > 1) and h(Ω) the Fréchet space of harmonic functions on Ω. Given a bounded linear operator L : h(Ω) → h(Ω), we show that its eigenvalues λn, arranged in decreasing order and counting multiplicities, satisfy |λn| ≤ K exp(−cn ), where K and c are two explicitly computable positive constants.

and Applied Analysis 3 The purpose of this paper is to present a general viscosity iteration process {xn}which is defined by xn 1 I − αnA Txn βnγf xn ( αn − βn ) xn 1.9 and to study the convergence of {xn}, where T is a nonexpansive mapping andA is a strongly positive linear operator, if {αn}, {βn} satisfy appropriate conditions, then iteration sequence {xn} converges strongly to the unique sol...

Consider the homogeneous equation u ′(t) = l(u)(t) for a.e. t ∈ [a, b] where l : C([a, b];R) → L([a, b];R) is a linear bounded operator. The efficient conditions guaranteeing that the solution set to the equation considered is one-dimensional, generated by a positive monotone function, are established. The results obtained are applied to get new efficient conditions sufficient for the solvabili...

In this paper we get the formula for the condition number of the W -weighted Drazin inverse solution of a linear system WAWx = b, where A is a bounded linear operator between Hilbert spaces X and Y , W is a bounded linear operator between Hilbert spaces Y and X, x is an unknown vector in the range of (AW ) and b is a vector in the range of (WA). AMS Mathematics Subject Classification (2000): 47...