Algebraic Properties of the Mikusiński Convolution Algebra

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Let M be the space of all continuous, complex valued functions defined on [0, ∞]. This, with the convolution operation (ƒg)(t) = ∫0t ƒ(t−τ)g(τ) dτ yields a commutative, associative algebra. A new proof that M is a Jacobson radical algebra is given. The ideal structures of M and its Dorroh extension to an algebra, M1, with unity are investigated. The algebraic properties of M are used to obtain new proofs of existence and uniqueness of solutions for certain integral and integro-differential equations.

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