Banded operators on coefficient sequences and the ultraspherical spectral method for linear differential equations.
Linear maps on polynomials as matrices acting on coefficient sequences, the language of ApproxFun.
The banded multiplication, differentiation and conversion matrices of the Jacobi and ultraspherical bases.
Linear differential equations with polynomial coefficients as exact almost-banded systems in ultraspherical bases.
Convergent finite solves for polynomial differential operators, under explicit bounded-boundary and infinite-operator invertibility assumptions.