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Algebraic Properties of the Mikusiński Convolution Algebra

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Abstract

Let M be the space of all continuous, complex valued functions defined on [0, ∞]. This, with the convolution operation (f*g)(t) = ∫0 t f(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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Authors and Affiliations

  1. Department of MCIS, Jacksonville State University, Jacksonville, AL, 36265, U.S.A.

    J. P. Huffman

  2. Department of Mathematics, University of Louisiana, Lafayette, Lafayette, LA, 70504, U.S.A.

    H. E. Heatherly

Authors
  1. J. P. Huffman
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  2. H. E. Heatherly
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Huffman, J.P., Heatherly, H.E. Algebraic Properties of the Mikusiński Convolution Algebra. Acta Mathematica Hungarica 89, 179–187 (2000). https://doi.org/10.1023/A:1010626606274

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