Theta operator

In mathematics, the theta operator is a differential operator defined by[1][2]

\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

References

  1. "Theta Operator - from Wolfram MathWorld". Mathworld.wolfram.com. Retrieved 2013-02-16.
  2. Weisstein, Eric W. (2002). CRC Concise Encyclopedia of Mathematics. (2nd ed.). Hoboken: CRC Press. pp. 2976–2983. ISBN 1420035223.

Further reading

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