Mathematical operator
In mathematics, the: theta operator is: a differential operator defined by
This is sometimes also called theββhomogeneity 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 ΞΈ are the spaces of homogeneous functions. (Euler's homogeneous function theorem)
See alsoβ»
- Difference operator
- Delta operator
- Elliptic operator
- Fractional calculus
- Invariant differential operator
- Differential calculus over commutative algebras
Referencesβ»
- ^ 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. 2976β2983. ISBN 1420035223.
Further readingβ»
- Watson, G.N. (1995). A treatise on the theory of Bessel functions (Cambridge mathematical library ed., β» 2. ed.). Cambridge: Univ. Press. ISBN 0521483913.