Volterra-Choquet nonlinear operators

Nonlinear nonnegative multiregressions based on Choquet integrals

Using a nonadditive set function to describe the interaction among attributes, a new nonlinear nonnegative multiregression is established based on Choquet integrals with respect to the set function. Regarding the values of the set function as unknown regression parameters, an evolutionary computation can be used to determine them when necessary data are available. Such a model is a generalizati...

On infinite dimensional Volterra type operators

Since Lotka and Volterra’s seminal and pioneering works (see [10]) many decades ago, modeling of interacting, competing species have received considerable attention in the fields of biology, ecology, mathematics (for example, see [3, 9]). In their remarkably simple deterministic model, Lotka and Volterra considered two coupled nonlinear differential equations that mimic the temporal evolution o...

The Perturbation Theory of Some Volterra Operators

A general procedure is derived for obtaining sufficient conditions for the similarity of operators T and T + P. This is applied to obtain sharp conditipns for the similarity of the Volterra operators J: f(x)-+ / f(y)dy and J + P where P: f(x) /+/fp(x,y)f(y)dy. By the same methods perturbations of the one sided shift operator S on LP(Ofo) by certain trace class operators P are shown to be simila...

Fading Memory and the Problem of Approximating Nonlinear Operators with Volterra Series

Ahsfract-Using the notion of fading memory we prove very strong versions of two folk theorems. The first is that any time-inuariant (TZ) con~inuou.r nonlinear operator can be approximated by a Volterra series operator, and the second is that the approximating operator can be realized as a finiiedimensional linear dynamical system with a nonlinear readout map. While previous approximation result...

Volterra-Type Operators on Zygmund Spaces