Analytical Foundations of Volterra Series

Analytical Foundations of Volterra Series

In this paper we carefully study the analysis involved with Volterra series. We address system-theoretic issues ranging from bounds on the gain and incremental gain of Volterra series operators to the existence of Volterra series operator inverses, and mathematical topics such as the relation between Volterra series operators and Taylor series. The proofs are complete, and use only the basic fa...

Analytical Treatment of Volterra Integro-Differential Equations of Fractional Derivatives

In this paper the solution of the Volterra integro-differential equations of fractional order is presented. The proposed method consists in constructing the functional series, sum of which determines the function giving the solution of considered problem. We derive conditions under which the solution series, constructed by the method is convergent. Some examples are presented to verify convergen...

Foundations of Computing Series

Volterra Series and Permutation Groups

shuffle product of the permutations u E E k and v' E E k, we mean the following element from ~+~, /,, (i), i < k , vmv'=: Z o'o(~,| where (v~v') ( i ) = ~ . v , ( i _ k ) + l e ' i ' > k . a(~sk+n'cn} Since the permutations form an additive basis of the space ~ , the shuffle multiplication is uniquely extended "by linearity" to any pair of elements from ~ and defines in $ = ~0$n a structure of ...

Volterra and Fliess Series Expansion