From Wikipedia, the free encyclopedia
Mathematical operator
In mathematics, the theta operator is a differential operator defined by[1][2]
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
[edit]- Difference operator
- Delta operator
- Elliptic operator
- Fractional calculus
- Invariant differential operator
- Differential calculus over commutative algebras
References
[edit]- ^ Weisstein, Eric W. "Theta Operator". MathWorld. Retrieved 2013-02-16.
- ^ Weisstein, Eric W. (2002). CRC Concise Encyclopedia of Mathematics (2nd ed.). Hoboken: CRC Press. pp. 2976–2983. ISBN 1420035223.
Further reading
[edit]- 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.
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