**The International Conference on
**

Secondary Calculus and Cohomological Physics,

Moscow, August 24 - August 31, 1997

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Secondary operational calculus

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Victor V. Zharinov

Steklov Mathematical Institute Gubkina 8, Moscow, GSP-1, 117966, Russia E-mail victor@zharinov.mian.su

**Abstract:** Outlines of operational calculus in differential algebras are given. By operational calculus we mean techniques reducing solution of linear differential equations with constant coefficients to solution of appropriate algebraic systems of linear equations. It is shown that in the classical differential algebra such techniques cannot be realized, because of the lack of nontrivial exponentials. At the same time, the differential Lie algebra of vertical derivations, possesses a full spectrum of exponentials, and the corresponding operational calculus (secondary operational calculus) is developed.

**Keywords:** Multiplicator, derivation, differential algebra, differential exponential, \f C$-differential operator

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