In mathematics, the theta operator is a differential operator defined by
This is sometimes also called the homogeneity operator, because its eigenfunctions are the monomials in z:
In n variables the homogeneity operator is given by
As in one variable, the eigenspaces of θ are the spaces of homogeneous polynomials.
- Watson, G.N. (1995). A treatise on the theory of Bessel functions (Cambridge mathematical library ed., [Nachdr. der] 2. ed.). Cambridge: Univ. Press. ISBN 0521483913.