Theta operator

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 functions. (Euler's homogeneous function theorem)

See also Difference operator Delta operator Elliptic operator Fractional calculus Invariant differential operator Differential calculus over commutative algebras

References

Further reading