ST type theory

In mathematics, the theta operator is a differential operator defined by

$\theta =z{d \over dz}$

This is sometimes also called the homogeneity operator, because its eigenfunctions are the monomials in z:

$\theta (z^{k})=kz^{k},\quad k=0,1,2,\dots$

In n variables the homogeneity operator is given by

$\theta =\sum _{k=1}^{n}x_{k}{\frac {\partial }{\partial x_{k}}}.$

As in one variable, the eigenspaces of θ are the spaces of homogeneous polynomials.

See also

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

References

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