Weierstrass polynomial


A function W:n of the form


where the aj are holomorphic functionsMathworldPlanetmath in a neighbourhood of the origin, which vanish at the origin, is called a Weierstrass polynomial.

Any codimension 1 complex analytic subvariety of n can be written as the zero set of a Weierstrass polynomial using the Weierstrass preparation theorem. This in general cannot be done for higher codimension.


  • 1 Lars Hörmander. , North-Holland Publishing Company, New York, New York, 1973.
  • 2 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
Title Weierstrass polynomial
Canonical name WeierstrassPolynomial
Date of creation 2013-03-22 15:04:25
Last modified on 2013-03-22 15:04:25
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 7
Author jirka (4157)
Entry type Definition
Classification msc 32A17
Classification msc 32B05
Synonym W-polynomial
Related topic Multifunction
Related topic WeierstrassPreparationTheorem