Slides of this talk (PDF)
The notion of integrodifferential algebra brings together the usual
derivation structure with an algebraic version of indefinite integration
and evaluation. We construct the associated algebra of
integrodifferential operators (used for modeling Green's operators for
linear boundary problems) directly in terms of normal forms. For
polynomial coefficients, we can use skew polynomials, defining the
integrodifferential Weyl algebra as a natural extension of the
classical Weyl algebra in one variable. Its algebraic properties and its
relation to the localization of differential operators are studied.
Fixing the integration constant, we regain the integrodifferential
operators with polynomial coefficients
