One fairly concrete setting for the mathematical research to be undertaken in this project is that of power series, which may be thought of as polynomials of infinite degree. Placing an appropriate constraint on the growth (or decay) of the coefficients of such a series gives rise to a Banach algebra of power series. It may happen that the only way to evaluate all of the series in the algebra is by taking the constant term. In this case, one has a (commutative) radical Banach algebra, a very exotic object. Recently, the principal investigator has proved an important result concerning derivations (analogues of the derivative in elementary calculus) of Banach algebras like these, thereby solving a problem that had been open for over thirty years. The techniques he developed will be extended and used to explore other structural questions.
