Approximation by strongly annular solutions of functional equations

Approximation of solutions to history-valued neutral functional differential equations

K e y w o r d s N e u t r a l functional differential equation, Analytic semigroup, Mild solution, FaedoGalerkin approximation. 1. I N T R O D U C T I O N Let H be a separable Hilbert space and 0 < T, T < ec. For 0 < t < T, Ct := C([-~-, t]; H) be the Banach space of all continuous functions from l--T, t] into H endowed with the supremum norm, Ilullt := sup I lu(s) l l , u • Ct, (1.1) -r<_s<t w...

Approximation in Uniform Norm by Solutions of Elliptic Differential Equations

Introduction. Let G be an open subset of the Euclidean w-space E, Gi an open subset with compact closure in G. If n = 2 and G is the whole of E, an important circle of theorems in the theory of analytic functions associated with the names of Walsh, HartogsRosenthal, Lavrentiev, Keldych, and Mergelyan deals with the possibility of approximating analytic functions on Gi continuous on its closure,...

Approximation of Solutions of Riccati Equations

This paper deals with two interrelated issues. One is an invariant subspace approach to finding solutions for the algebraic Riccati equation for a class of infinite dimensional systems. The second is approximation of the solution of the algebraic Riccati equation by finite dimensional approximants. The theory of exponentially dichotomous operators and bisemigroups is instrumental in our approach.

Multiple Positive Radial Solutions for Quasilinear Equations in Annular Domains

Asymptotically Optimal Approximation and Numerical Solutions of Diierential Equations Asymptotically Optimal Approximation and Numerical Solutions of Diierential Equations

Given nite subset J IR n , and a point 2 IR n , we study in this paper the possible convergence, as h ! 0, of the coeecients in least-squares approximation to f(+hh) from the space spanned by (f(+ hj) j2J. We invoke thèleast solution of the polynomial interpolation problem' to show that the coeecient do converge for a generic J and , provided that the underlying function f is suuciently smooth....