Operational calculus in differential algebras

^∗ This work was supported by RBRF under Grant n. 95-01-00027

^∗

Abstract

Outlines of operational calculus i.e., techniques, reducing the solution of linear differential equations with constant coefficients to the solution of appropriate algebraic systems of linear equations, in differential algebras are described. It is shown that in the classical differential algebra such techniques cannot be realized, because of the lack of non-trivial 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
• ζ-differential operator

MSC(1991):

• 44A
• 35A
• 49E

^∗ This work was supported by RBRF under Grant n. 95-01-00027

^∗ This work was supported by RBRF under Grant n. 95-01-00027

Notes

^∗ This work was supported by RBRF under Grant n. 95-01-00027

Additional information

Notes on contributors

Victor V. Zharinov