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Math Help - Division by a polynomial

  1. #1
    Member
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    Division by a polynomial

    Hello,

    in a paper i have read this:

    Consider the Equation PT=S , whereas P is some polynomial of derivation. Then for any smooth function S we can find a smooth function T, s.t. this equation is satisfied.

    Then the author says:
    " This means that division, in the sense of convolution multiplication, by a polynomial of derivation is always possible".

    What does this sentence mean? For polynomials there is no division in general. Therefore the author mean indeed "convolution multiplication". But i don't know what this expression actually means? I know what a convolution of two given functions is. Also what a multiplication is. But not the synthesis like above.

    Regards
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  2. #2
    Grand Panjandrum
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    Re: Division by a polynomial

    Quote Originally Posted by Sogan View Post
    Hello,

    in a paper i have read this:

    Consider the Equation PT=S , whereas P is some polynomial of derivation. Then for any smooth function S we can find a smooth function T, s.t. this equation is satisfied.

    Then the author says:
    " This means that division, in the sense of convolution multiplication, by a polynomial of derivation is always possible".

    What does this sentence mean? For polynomials there is no division in general. Therefore the author mean indeed "convolution multiplication". But i don't know what this expression actually means? I know what a convolution of two given functions is. Also what a multiplication is. But not the synthesis like above.

    Regards
    Is this by any chance connected with Laplace Transforms?

    (the inverse of a polynomial in the differential operator in this sense still requires initial conditions for uniqueness)


    CB
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