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Русская версия

**Adel Kassaian**

University of British Columbia 2004

General formula for causal Green's function of linear differential operator of given degree in one variable is given according to coefficient functions of differential operator as a series of integrals. The solution also provides analytic formula for fundamental solutions of corresponding homogenous linear differential equation, Furthermore, multiplicative property of causal Green's functions is shown and by which explicit formulas for causal Green's functions of some classes of decomposable linear differential operators are given. A method to find Green's function of general linear differential operator of given degree in one variable with arbitrary boundary condition according to coefficient functions of differential operator is demonstrated.

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- Harry Hochstadt, Integral equations, pp. 330, Wiley, 1973
- Tarjan, Lalesco, Theorie Des Equations Integrales, pp. 125, Herman and fils, Paris, 1912