Ukrainian Mathematical Bulletin

Volume 2, Issue 3, 2005 pp. 425-448.

Approximation of Nonlinear Operators by Volterra Series in the Multidimensional Case

Authors: Sergei G. Suvorov
Author institution: Institute of Applied Mathematics and Mechanics of NAS of Ukraine, 74 Rosa Luxemburg Str., 83114, Donetsk, Ukraine

Summary: We consider continuous nonlinear operators $A\,:\,X\rightarrow Y$ acting from a functional locally convex space $X$ into a normed functional space $Y$. The elements of $X$ and $Y$ are functions of many variables. A~general theorem on the approximation of $A$ by Volterra series is proved in a simple way. For equivariant operators (with respect to the translation group or the isometry group) and for causal operators, we prove the possibility of their approximation by Volterra series with the same properties of equiinvariance or causality.

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