In the present paper we introduce a certain family of linear positive operators and study some direct results which include a pointwise convergence, asymptotic formula and an estimation of error in simultaneous approximation.

In this document I develop a weight function theory of zero order basis function interpolants and smoothers. In Chapter 1 the basis functions and data spaces are defined directly using weight functions. The data spaces are used to formulate the variational problems which define the interpolants and smoothers discussed in later chapters. The theory is illustrated using some standard examples of ...

In this paper the boundaries of several families of (time-invariant) ARMA models and corresponding linear state space models are described. The topology of pointwise convergence of the Markov parameters is used.