Using the notion of fading memory we prove very strong versions of two folk theorems. The
first is that any time-invariant (TI) continuous nonlinear operator can be approximated by a …

The fundamental importance of functional differential equations has been recognized in
many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional …

During the past five years, multilinear, multipower, and polynomic systems have become a
most important area of applications and theoretical development. This paper starts with …

This article examines the application of regularization techniques and kernel methods in
addressing the task of learning nonlinear dynamical systems from input–output data. Our …

Several structural features are investigated for the class of systems K composed of K linear
dynamic subsystems connected in parallel with outputs multiplied (in the time domain) …

An approximation theorem is given for causal time‐invariant nonlinear maps that take one
set of functions defined on [0,∞) into another. The theorem is used to show that, under some …

Non-Selfadjoint Operator Algebras Page 1 NON-SELFADJOINT OPERATOR ALGEBRAS By JA
ERDOS Department of Mathematics, King's College, London WC2R 2LS Communicated by TT …

Let K denote an arbitrary compact subset of real L 2. Let f be any causal continuous function
on L 2. Then there is a linear differential system: ż (t)= A (t) z (t)+ B (t) u (t), and a memoryless …

In this paper, we provide a state-of-the-art survey of some recent methods in nonlinear
operator approximation theory and its applications. We give existence theorems for …

Approximation of the input-output behavior of nonlinear systems characterized by fading
memory properties is addressed. System structures are proposed as approximants along …